- ology from graph theory. In fact some of these problems had already been studied in graph theory before they appeared in the context of parallel computing. A graph has two key components: The vertex set , which is just a list of indices; The edge set . Each.
- A
**graph**G consists of two sets of items: vertices (V) & edges (E). In other words, a**graph**G = <V,E>. Simple**Graphs**— Set**Notation**In this article, in contrast to the opening piece of this series, we'll work though**graph**examples - In graph theory, the most frequently used notations for the set of vertices and the set of edges are Vand E, respectively. Furthermore, G(V,E) denotes the graph itself. The square of a graph, whose definition is explained below, is represented by G2. On this website, these notations will be maintained
- Graph theory is the study of graphs, systems of nodes or vertices connected in pairs by edges
- I am writing a TeX document with some graph theory notation and there is some notation I couldn't get: I checked in Word and it's Cambria Math font, but when I used the {unicode-math} package it . Stack Exchange Network. Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and.

Basic Graph Theory De nitions and Notation continued paths and cycles walk v 0e 1v 1e 2:::e kv k where e i = v i 1v i, 81 i k (often written as v 0v 1:::v k) endpoints: v 0;v k length: k(or P k i=1 w(e i) if Ghas edge weights w: E7!R) closed if v 0 = v k Note: edges and vertices may be repeated trail a walk with no repeated edge path a trail with no repeated vertex (unless closed { then v 0. A graph G is an ordered pair (V, E), where V is a finite set and graph, G E ⊆(V 2) is a set of pairs of elements in V. •The set V is called the set of vertex, edgevertices and E is called the set of edges of G. •The edge e = {u,v}∈(V 2) is also denoted by e = uv A graph 'G' is defined as G = (V, E) Where V is a set of all vertices and E is a set of all edges in the graph. Example 1 In the above example, ab, ac, cd, and bd are the edges of the graph. Similarly, a, b, c, and d are the vertices of the graph

* Discrete Mathematics*, Spring 2009 Graph theory notation David Galvin March 5, 2009 Graph: a graph is a pair G = (V;E) with V a set of vertices and Ea set of edges — (unordered) pairs of vertices Ein Graph (selten auch Graf) ist in der Graphentheorie eine abstrakte Struktur, die eine Menge von Objekten zusammen mit den zwischen diesen Objekten bestehenden Verbindungen repräsentiert. Die mathematischen Abstraktionen der Objekte werden dabei Knoten (auch Ecken) des Graphen genannt

Let's move straight into graph theory. An undirected graph G = (V, E) consists of a set of vertices V and a set of edges. It is an undirected graph because the edges do not have any direction. Each.. A graph with six vertices and seven edges. In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense related. The objects correspond to mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line) 2 Notations 3 3 Preliminaries 4 4 Matchings 13 5 Connectivity 16 6 Planar graphs 20 7 Colorings 25 8 Extremal graph theory 27 9 Ramsey theory 31 10 Flows 34 11 Random graphs 36 12 Hamiltonian cycles 38 References 39 Index 40 2. 1 Introduction These brief notes include major de nitions and theorems of the graph theory lecture held by Prof. Maria Axenovich at KIT in the winter term 2013/14. We.

- For the history of early graph theory, see N.L. BIGGS, R.J. LLOYD ANDR.J. WILSON, Graph Theory 1736 - 1936, Clarendon Press, 1986. There are no standard notations for graph theoretical objects. This is natural, be- cause the names one usesfor the objects reﬂect the applications
- Graph Theory Notes Vadim Lozin Institute of Mathematics University of Warwick 1 Introduction A graph G= (V;E) consists of two sets V and E. The elements of V are called the vertices and the elements of Ethe edges of G. Each edge is a pair of vertices. For instance, the sets V = f1;2;3;4;5gand E = ff1;2g;f2;3g;f3;4g;f4;5ggde ne a graph with 5 vertices and 4 edges. Graphs have natural visual.
- I am new to set theory and graph theory but have been asked to provide a formal model and so I'm on a steep learning curve. Having got my head around a lot of the notation I am struggling with the . Stack Exchange Network. Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge.

Graph Theory - Types of Graphs - There are various types of graphs depending upon the number of vertices, number of edges, interconnectivity, and their overall structure. We will discuss only Browse other questions tagged graph-theory notation or ask your own question. Featured on Meta Feedback post: New moderator reinstatement and appeal process revisions. The new moderator agreement is now live for moderators to accept across the Related. Question feed Subscribe to RSS. graph-theory notation multigraphs. share | cite | improve this question | follow | edited Mar 20 at 20:24. MScott. asked Mar 20 at 18:29. MScott MScott. 11 2 2 bronze badges $\endgroup$ 1 $\begingroup$ Can you give the source? $\endgroup$ - CyclotomicField Mar 20 at 19:22 $\begingroup$ As @CyclotomicField suggests, knowing the source of this notation would be helpful. That being said, the.

A quick guide to some important mathematical notation, especially for discrete math, combinatorics and graph theory. I use small examples to review notation used in counting, set theory, summation. Modern Graph Theory by Bollob¶as (1998) for terminology and notation which are not deﬂned here. We assume that the readers have read some standard textbooks in graph theory, a few of which are listed at the end of this chapter. Let G = (V;E) be a graph with vertex set V = V(G) and E = E(G). The number of vertices of V is called the order of G, which is the size of V. The size of E(G) is.

Jul 23, 2017 - Explore Sally Utley's board Graphic Notation, followed by 779 people on Pinterest. See more ideas about Notations, Graphic score, Music composition * Graph Theory - Notation (Mathematical Representation) If you read the What is Graph ? page, you might have thougt 'Ohm*.. it is interesting concept. it doesn't look as hard and boring as other mathematical topics'. and if you went through 'Terminology' page, 'Pretty many technical words.. but I think I can digest it to some degree', but Graph Theory is also a part (branch) of mathematics. The. Zusammenhang (Graphentheorie) Ein zusammenhängender Graph: Je zwei Knoten lassen sich durch eine Kantenfolge verbinden. Exemplarisch ist eine Kantenfolge zwischen den Knoten v und w rot hervorgehoben. Der Zusammenhang ist ein mathematischer Begriff aus der Graphentheorie

Graph Theory Notations DRAFT. a year ago. by hollandmath22. Played 63 times. 0. 12th grade . Mathematics. 58% average accuracy. 0. Save. Edit. Edit. Print; Share; Edit; Delete; Host a game. Live Game Live. Homework. Solo Practice. Practice. Play. Share practice link. Finish Editing. This quiz is incomplete! To play this quiz, please finish editing it. Delete Quiz. This quiz is incomplete! To. We can only move the knights in a clockwise or counter-clockwise manner on the graph (If two vertices are connected on the graph: it means that a corresponding knight's move exists on the grid). However the order in which knights appear on the graph cannot be changed. There is no possible way for a knight to cross over (Two knights cannot exist on one vertex) the other in order to achieve. A graph is a data structure that is defined by two components : A node or a vertex.; An edge E or ordered pair is a connection between two nodes u,v that is identified by unique pair(u,v). The pair (u,v) is ordered because (u,v) is not same as (v,u) in case of directed graph.The edge may have a weight or is set to one in case of unweighted graph Section 2: Notation 8 2. Notation To formalize our discussion of graph theory, we'll need to introduce some terminology. A graph G is a pair of sets V and E together with a function f: E 7!V ‡ V.The elements of V are the vertices (a.k.a. nodes or points) of G.The elements of E are the edges of G.The function f sends an edge to the pair of vertices that are its endpoints, thus f i Graphs. It's all about relationships. Objectives. Use Graph Theory vocabulary; Use Graph Theory Notation; Model Real World Relationships with Graphs; You'll revisit these! You need:.

Subscribe to this blog. Follow by Email Random GO Graph theory is the study of mathematical objects known as graphs, which consist of vertices (or nodes) connected by edges. (In the figure below, the vertices are the numbered circles, and the edges join the vertices.) A basic graph of 3-Cycle. Any scenario in which one wishes to examine the structure of a network of connected objects is potentially a problem for graph theory Graph theory notation code bricks for JavaScript. Contribute to aureooms/js-graph-theory-notation development by creating an account on GitHub In Figure 5.8, we show a graph and one of its spanning trees. We will return to the subject of spanning trees in Chapter 12. <<SVG image is unavailable, or your browser cannot render it>> Figure 5.8 A Graph and a Spanning Tree. The following theorem is very elementary, and some authors refer to it as the first theorem of graph theory. 301 Moved Permanently. ngin

focused on spectral graph theory to provide technical details not covered in class and to help you with parts of the nal homework. This handout only covers a small fraction of graph clustering techniques. For a more comprehensive review, see some of the survey papers on the topic [3,4,6]. 1 Matrix notation and preliminaries from spectral graph theory Spectral graph theory studies properties of. Provides an implementation of Graph Theory graph G = (V, E), that can generate its DOT notation, which can be used for rendering the graph. - etmendz/Mendz.Graph Graph Theory: Intro and Trees CS 2800: Discrete Structures, Spring 2015 Sid Chaudhuri. This is ok (Ok because equality is symmetric and transitive) This is NOT ok ⇒ ⇒ ⇒ ⇒ T ⇒ h e s e ⇒ s y m b o l s a r e i m p l i e d i f y o u o m i t t h e m which is true, so QED No! Plea for the Day #1 Please read out your proofs in plain English and ask yourself if it makes sense http. This video gives an overview of the mathematical definition of a graph. It gives some basic examples and some motivation about why to study graph theory

WARNING: This project has been renamed to @aureooms/js-graph-theory-notation. Last updated 5 years ago by aureooms. AGPL-3.0 · Repository · Bugs · Original npm · Tarball · package.json $ cnpm install aureooms-js-graph-theory-notation . SYNC missed versions from official npm. The following video describes: Set Notations, Empty Set, Symbols for ҩs an element ofҬ subset, intersection and union. Show Step-by-step Solutions. Set Notation Roster Method, Set Builder Notation. Show Step-by-step Solutions. Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step. on notation, MM', graph theory, incidence matrix product Showing 1-3 of 3 messages. on notation, MM', graph theory, incidence matrix product: Daniel Bastos: 9/16/17 7:27 AM: Problem. Show that if G is simple, the entries on the diagonals of both MM' and A^2 are the degrees of the vertices of G. I don't understand what is meant by MM'. M is the incidence matrix of graph G. By looking at section.

History of Graph Theory Graph Theory started with the Seven Bridges of Königsberg. The city of KÃ¶nigsberg (formerly part of Prussia now called Kaliningrad in Russia) spread on both sides of the Pregel River, and included two large islands which were connected to each other and the mainland by seven bridges. The problem - bothering the inhabitants - having a walk through the city, but. Prerequisite: Asymptotic Notations Assuming f(n), g(n) and h(n) be asymptotic functions the mathematical definitions are: If f(n) = Θ(g(n)), then there exists positive constants c1, c2, n0 such that 0 ≤ c1.g(n) ≤ f(n) ≤ c2.g(n), for all n ≥ n0; If f(n) = O(g(n)), then there exists positive constants c, n0 such that 0 ≤ f(n) ≤ c.g(n), for all n ≥ n Graph theory is a relatively new branch of mathematics which deals with the study of objects named graphs. These types of graphs are not of the variety with an x- and y-axis, but rather are made up of vertices, usually represented as points, and edges, usually thought of as lines in between two vertices. For example, the following are examples of graphs: P3 K5 K3,3 P3, called the path on 3.

- Algorithmic Complexity and Big-O Notation. The graph below compares the running times of various algorithms. Linear -- O(n) Quadratic -- O(n 2) Cubic -- O(n 3) Logarithmic -- O(log n) Exponential -- O(2 n) Square root -- O(sqrt n) Comparison of algorithms in terms of the maximum problem size they can handle: Algorithm Complexity: Running time T(n) (measured in seconds on an Apple Delicious.
- Graph Theory and Trees Graphs A graph is a set of nodes which represent objects or operations, and vertices which represent links between the nodes. The following is an example of a graph because is contains nodes connected by links. Node / Vertex A node or vertex is commonly represented with a dot or circle. The node itself often represents something else, such as data, or an operation or.
- We've partnered with Dartmouth college professors Tom Cormen and Devin Balkcom to teach introductory computer science algorithms, including searching, sorting, recursion, and graph theory. Learn with a combination of articles, visualizations, quizzes, and coding challenges
- Set theory notation - help. Thread starter brennan; Start date Oct 26, 2010; Tags notation set theory; Home. Forums. University Math Help. Discrete Math . B. brennan. Oct 2010 23 1. Oct 26, 2010 #1 I am self studying graph theory - and a book has the notation: The set \(\displaystyle Z/nZ\) of intagers modulo n is written Zn (if you know how to use Latex to write the n as postscript characters.

- View graph 1.pdf from MATH 0011 at The University of Hong Kong. Chapter 1: Graphs and Networks 1.3 Notation and Basic Deﬁnitions Deﬁnition 1.3.1: A graph is an ordered triple G = (V, E, ϕ)
- I googled it and apparently they are commonly used in group theory, which does not make much sense to me here. Thanks for your input. btw: The paper is called A Formal Definition of Data Flow Graph Models by Kavi, Buckles and Bhat, and is available here
- In der Kombinatorik als Teilgebiet der diskreten Mathematik ist die Lederberg-Coxeter-Fruchte-Notation (kurz LCF) eine kompakte Darstellung endlicher kubischer hamiltonscher Graphen.Die Notation geht auf Joshua Lederberg zurück und wurde von H. S. M. Coxeter und Robert Frucht erweitert. Viele Programme zur Manipulation von Graphen unterstützen LCF-Eingaben
- Using basic group theory, the reason these solutions are not incredibly diﬃcult to ﬁnd will become clear. Notation Throughout this discussion, we will use the following notation to refer to the sides of the cube: Front F Right R Down D Up U Left L Back B 1. SP.268 The Mathematics of the Rubik's Cube The same notation will be used to refer to face rotations. For example, F means to rotate.
- The main idea of asymptotic analysis is to have a measure of efficiency of algorithms that doesn't depend on machine specific constants, mainly because this analysis doesn't require algorithms to be implemented and time taken by programs to be compared. We have already discussed Three main asymptotic notations.The following 2 more asymptotic notations are used to represent time complexity.

Graph theory: Shortest average path length, notation problem [undergraduate level] Close. 3. Posted by. u/derlumpenhund . 6 years ago. Archived. Graph theory: Shortest average path length, notation problem [undergraduate level] I have a very basic notation question regarding calculation of the shortest average pathlength of an undirected network. The formula I know is: L = N(N-1)/SUM(d_i,j. Graph theory does not solve this problem but it can provide some interesting perspectives. mcs-ftl — 2010/9/8 — 0:40 — page 193 — #199 6.2. Tournament Graphs b d c e f Figure 6.4 A 5-node tournament graph. The results of a round-robin tournament can be represented with a tournament graph. This is a directed graph in which the vertices represent players and the edges indicate the. Notation We follow the basic graph theory notation from the book of Bondy and Murty [1]. For a graph G, we denote the set of vertices of Gby V(G) and the set of edges of Gby E(G) V(G) 2. We call the cardinality of V(H) the order of Hand denote it by v(H), and the cardinality of E(H) the size of Hand denote it by e(H). For a graph H, we denote by H the complement of H, i.e., the graph with the. Use Graph Theory vocabulary and notation; Discuss different types of search and benefits of each; GRAPHS. GRAPH THEORY VOCAB. Graph. Graphs are a very common nonlinear data structure in computer science. Graphs are common because it's very easy to describe a lot of real world problems in the language of Graph Theory. GRAPH THEORY VOCAB . G = (V, E) Vertice (node): circles on the graph. Start studying Graph Theory - Basic Notation. Learn vocabulary, terms, and more with flashcards, games, and other study tools

Abstract: Supervisory control of the mobile robot navigation system has critical importance. The supervisory control software development of mobile robot navigation can be performed in an unknown environment or for controlled robots in a know Schoolwork101.com Logic and Proofs Propositions Conditional Propositions and Logical Equivalence Quantifiers Proofs Mathematical Induction The Language of Mathematics Sets Sequences and Strings Relations Equivalence Relations Matrices of Relations Relational Databases Functions Algorithms Introduction to Algorithms Notation for Algorithms The Euclidean Algorithm Recursive Algorithms Complexity. In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense related. The objects correspond to mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line)

Just wanted to know, for example in the wikipedia page Dijkstra's algorithm what the absolute value bars meant in O(|E| + |V|log|V| Apr 16, 2020 - Graphic notation is the representation of music through the use of visual symbols outside the realm of traditional music notation. Graphic notation evolved in the 1950s, and it is often used in combination with traditional music notation. Composers often rely on graphic notation in experimental music, where standard musical notation can be ineffective 1/2absinC 3D shapes Adding algebraic fractions Adding and subtracting vectors Adding decimals Adding fractions Adding negative numbers Adding surds Algebraic fractions Algebraic indices Algebraic notation Algebraic proof Alternate angles Alternate segment theorem Angle at the centre Angle in a semi-circle Angles Angles at a point Angles in a. * This course covers elementary discrete mathematics for computer science and engineering*. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting.

Graph Theory. For (a), The notation G-e means the graph G with edge e removed. Show transcribed image text. Expert Answer 100% (2 ratings) Previous question Next question Transcribed Image Text from this Question. Give an example or explain why no such example exists. For the examples, please briefly verify that they satisfy the conditions given. (a) A semi-Eulerian graph G with an edge e such. focused on spectral graph theory to provide technical details not covered in class and to help you with parts of the nal homework. This handout only covers a small fraction of graph clustering techniques. For a more comprehensive review, see some of the survey papers on the topic [3,4,7]. 1 Matrix notation and preliminaries from spectral graph theory Spectral graph theory studies properties of. * May 30*, 2012 - Sketches showing Penderecki's graphic approach to notation @MISC{_tablei., author = {}, title = {TABLE I. NOTATIONS IN GRAPH THEORY Symbol Meaning}, year = {}} Share. OpenURL . Abstract. V (G), L(G) set of nodes/links in graph G |G | degree of G: |G | = |V (G) | (number of nodes) ||G| | order of G: ||G| | = |L(G) | (number of links) G ∪ G ′ union of graphs: G ∪ G ′ = (V ∪ V ′ ; L ∪ L ′) H interior graph P simple path mi mi ∈ V (G) is.

abbreviated notation), S 2 = {12,13,23}, S 2 = {11,22,33,12,13,23}. We now deﬁne what is meant by a graph. Intuitively, graphs have vertices and edges, where each edge connects two vertices (which may be the same). It is possible for two diﬀerent edges eand e′ to connect the same two vertices Just ran into this notation and I'm not familiar with it. I've seen `min(x)` and `max(x)` before but this is a..

- Mathematical Notation Graphs Chapter 4 Graph. Use WinPlot to create the graph to the right. - If you had Use Defaults checked when you created the graph, then this step should be optional as the default viewing window is -5 to 5 for both the x and y directions. Click Set Center; The horizontal center is 0; The vertical center is 0; The width is 10 (that gives you five on either side) Click.
- istration: Amazon.de: Kindle-Sho
- The Musical Timespace. I: Notation Examples & Graphs. II: A Theory of Music Listening. [2 Vols.9. | Erik Christensen | ISBN: | Kostenloser Versand für alle Bücher mit Versand und Verkauf duch Amazon
- ology for Graphs; Multigraphs: Loops and Multiple Edges; Eulerian and Hamiltonian Graphs; Graph Coloring; Planar Graphs; Counting Labeled Trees; A Digression into Complexity Theory; Discussion; Exercises; 6 Partially Ordered Sets. Basic Notation and Ter
- Sequences, Probability, and Counting Theory. Series and Their Notations Learning Objectives. Use summation notation. Use the formula for the sum of the ﬁrst n terms of an arithmetic series. Use the formula for the sum of the ﬁrst n terms of a geometric series. Use the formula for the sum of an inﬁnite geometric series. Solve annuity problems. A couple decides to start a college fund for.
- g theory is something that transcends a single program
- LCF-Notationen zu einem Graphen sind im Allgemeinen nicht eindeutig bestimmt. Sie hängen von der Wahl des Startknotens \({\displaystyle v_{0}}\) und von der Wahl des Hamiltonkreises ab (dort hat man stets wenigstens die Wahl einer Orientierung). Umgekehrt kann es aber zu jeder LCF-Notation nur einen, bis auf Isomorphie, eindeutigen Graphen geben. Stellt man LCF-Code zusammen mit einem Plot.

Download Citation | Kinematic Analysis of Bevel Epicyclic Gear Trains Using Graph Notation | A kinematic analysis technique is introduced to find the velocities of all links in bevel epicyclic. Horrible notation you don't need to remember. A walk that doesn't repeat any edges is a trail. A walk that doesn't repeat any vertices is a path. Actually, we allow paths to have the first and last vertex be the same, so that we can have closed paths . Konigsberg revisted Definition of an Eulerian graph. A graph $\Gamma$ is Eulerian if it has a walk that uses every edge exactly once. Is the. What do the absolute value bars mean in graph theory? Ask Question Asked 7 years, 4 months ago. Active 7 years, 4 months ago. Viewed 2k times 4. 1. Just wanted to know, for example in the wikipedia page Dijkstra's algorithm what the absolute value bars meant in O(|E| + |V|log|V|) notation. share | improve this question | follow | asked Feb 23 '13 at 6:08. William Rookwood William Rookwood. 257. ** Do you mean this notation: [math]{n \choose k}[/math] That denotes the number of different ways we can choose a set of[math]k[/math] different elements from a set of [math]n[/math] elements (note that we pick a set of [math]k[/math] elements, so o**.. Graphs also happen to represent category theory diagrams so perhaps we can find a way to relate the internal structure of graph objects to the category theory relationship of objects and arrows. Category diagram for Graph

** Graph Theory dates back to times of Euler when he solved the Konigsberg bridge problem**. Any graph can be seen as collection of nodes connected through edges. Mathematically this is represented as G = [V,E] (a notation, nothing to worry about if it.. Graphic notation is one side that is relatively unknown outside the sometimes rarefied world of orchestral and experimental music. Composers have always grappled with ways to express themselves and in the twentieth-century, several began using this radical graphical approach to writing scores. It was a two-fingered salute to the prevailing musical establishment. Graphic notation functions the. Four Color Theorem Every planar graph can be colored using no more than four colors. graph Informally, a graph is a finite set of dots called vertices (or nodes) connected by links called edges (or arcs). More formally: a simple graph is a (usually finite) set of vertices V and set of unordered pairs of distinct elements of V called edges. Not.

Graph Theory - History Arthur Cayley James J. Sylvester George Polya Enumeration of Chemical Isomers Graph Theory - History Francis Guthrie Auguste DeMorgan Four Colors of Maps. Definition: Graph •G is an ordered triple G:=(V, E, f) -V is a set of nodes, points, or vertices. -E is a set, whose elements are known as edges or lines. -f is a function •maps each element of E •to an. View GraphTheoryGloss.pdf from AA 11 Wasserman and Faust, Chapter 3: **Notation** for Social Network Data Original by Catherine Bailey Specific **notation** allows network concepts (actors, relations betwee ** 8**.graph notations_工学_高等教育_教育专区 16人阅读|2次下载.** 8**.graph notations_工学_高等教育_教育专区。Discrete Mathematics and Its Application Graph: Notations Fundamental Concept

Graphic notation: | |Graphic notation| is the representation of music through the use of visual symbols outsi... World Heritage Encyclopedia, the aggregation of the largest online encyclopedias available, and the most definitive collection ever assembled Kinematic analysis of bevel epicyclic gear trains using graph notation. Carl A. Nelson, Raymond J. Cipra. Mechanical & Materials Engineering; Research output: Contribution to conference › Paper. 3 Citations (Scopus) Abstract. A kinematic analysis technique is introduced to find the velocities of all links in bevel epicyclic gear trains. The method relies on previous work in graph theory. It. Jul 23, 2017 - Explore Sally Utley's board Graphic Notation, followed by 741 people on Pinterest. See more ideas about Notations, Graphic score, Music composition