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  1. math.libretexts.org › Bookshelves › Combinatorics_and5.1: The Basics of Graph Theory - Mathematics LibreTexts

    Figure 5.1.1 5.1. 1: A simple graph. A graph G = (V, E) G = (V, E) that is not simple can be represented by using multisets: a loop is a multiset {v, v} = {2 ⋅ v} {v, v} = {2 ⋅ v} and multiple edges are represented by making E E a multiset. The condensation of a multigraph may be formed by interpreting the multiset E E as a set.

  2. www.geeksforgeeks.org › walks-trails-paths-cyclesWalks, Trails, Paths, Cycles and Circuits in Graph

    Sep 20, 2024 · Prerequisite: Graph Theory Basics – Set 1, Set 2 Regular Graph: A graph is called regular graph if degree of each vertex is equal. A graph is called K regular if degree of each vertex in the graph is K. Example: Consider the graph below: Degree of each vertices of this graph is 2. So, the graph is 2 Regular. Similarly, below graphs are 3 ...

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    • Learning Curve: Theory, Meaning, Formula, Graphs [2022]
    • Learning Curve: Theory, Meaning, Formula, Graphs [2022]
    • Learning Curve: Definition, Theory (Graphs), And Examples
    • Learning Curve: Definition, Theory (Graphs), And Examples

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  4. www.geeksforgeeks.org › mathematics-graph-theoryMathematics | Graph Theory Basics - Set 2 - GeeksforGeeks

    • Graph Theory Basics
    • Types of Graph
    • Basic Graph Terminology
    • Some Special Simple Graphs
    • Examples
    • Summary
    • Gate CS Corner Questions

    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 of the graph correspond to verticesand the relations between them correspond to edges. A graph is depicted diagrammatically as a set of dots depicting vertices connected by lines or curves depicting edges. Formally, “A gr...

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    There are several types of graphs distinguished on the basis of edges, their direction, their weight etc. 1. Simple graph:A graph in which each edge connects two differentvertices and where no two edges connect the same pair of vertices is called a simple graph. For example, Consider the following graph – The above graph is a simple graph, since no...

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    In the above discussion some terms regarding graphs have already been explained such as vertices, edges, directed and undirected edges etc. There are more terms which describe properties of vertices and edges. 1. Adjacency: In a graph GG Gtwo vertices uu uand vv vare said to be adjacentif they are the endpoints of an edge. The edge {u,v}–e\{u, v\} ...

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    1. Complete Graphs:A simple graph of nn nvertices having exactly one edge between each pair of vertices is called a complete graph. A complete graph of nn nvertices is denoted by KnK_{n} Kn​. Total number of edges are n*(n-1)/2 with n vertices in complete graph. 2. Cycles:Cycles are simple graphs with vertices n≥3n \geq 3 n≥3 and edges {1,2}, {2,3}...

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    Simple Graph:Let us take the example of graph that has vertices say {A, B, C, D} and the edges labelled as (A, B), (B, C), (C, D), and (D, A). This is connected and simple graph because there are n...
    Multigraph:For instance if there are two arrows connecting A and B and one arrow between B and C, then this diagram is a multigraph.
    Directed Graph:In the case of a directed graph there could be a directed arc from A to B and another from B to C.
    Complete Bipartite Graph: In one set there should be 3 vertices namely A, B and C; while in the other set there should be only two vertices, namely X and Y. Another graph is complete bipartite grap...

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    Graph theory provides a framework for modeling relationships and connections in various fields. The types of graphs and key properties such as adjacency, degrees, and the handshaking theorem are crucial in understanding the structure and behavior of graphs. By solving problems in graph theory, we gain insights into the complexity and patterns in da...

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    Practicing the following questions will help you test your knowledge. All questions have been asked in GATE in previous years or in GATE Mock Tests. It is highly recommended that you practice them. 1. GATE CS 2013, Question 25 2. GATE CS 2014 Set-1, Question 61 3. GATE CS 2006, Question 71 4. GATE CS 2002, Question 25 5. GATE CS 2004, Question 37 6...

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  5. web.math.princeton.edu › math_alive › 5Math Alive Graphs 1 - Princeton University

    Basics of Graph Theory. The basic objects in graph theory are graphs. A graph is a slightly abstract represention of some objects that are related to each other in some way, and of these relationships. The objects are drawn as dots called vertices; a line (or curve) connects any two vertices representing objects that are related or adjacent ...

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  7. www.mathsisfun.com › sets › graph-theoryIntroduction to Graph Theory - Math is Fun

    Graph Theory studies how things are connected, through a network of points and lines. A graph looks like this: An Example Graph. Yes, it is called a "graph"... but it is NOT this kind of graph: They are both called "graphs". But they are different things. Just how it is. This subject explores how these points and lines relate to each other, and ...

  8. math.stackexchange.com › questions › 2331721graph theory - Definition of a curve (Jordan Curve Theorem ...

    Jun 21, 2017 · 3. You got it correctly -- the JCT says that a closed non-self-intersecting curve partitions the rest of the plane into inside and outside. Continuous image means that there is a continuous function f: C(0, 1) →R2 f: C (0, 1) → R 2, where your closed curve is the image of f f (where C(0, 1) C (0, 1) denotes the unit circle). Share. Cite ...

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  10. www.geeksforgeeks.org › fundamentals-of-graph-theoryFundamentals of Graph Theory - GeeksforGeeks

    Aug 5, 2024 · Applications of Graph Theory: In mathematics and computer science, a graph is a mathematical structure that consists of two main components: vertices (or nodes) and edges. The study of these graphs in various contexts is called graph theory. There are various applications of graph theory in real life such as in computer graphics and networks, biolo

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