basic definitions of graph theory with examples pdf
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Basic graph theory
This Figure 1 2: Planar non-planar and dual graphs (a) Plane ‘butterfly’graph construction can (b be c) iterated Non- to obtain higher-order line (or derivative) graphs planar graphs (d) The two red graphs are both dual to the blue graph but they are not isomorphic Image source: wiki 1 3 Adjacency and incidence |
What is graph theory?
It is a sub-field of mathematics which deals with graphs: diagrams that involve points and lines and which often pictorially represent mathematical truths. Graph theory is the study of the relationship between edges and vertices. Formally, a graph is a pair (V, E), where V is a finite set of vertices and E a finite set of edges.
Why do we call a graph a general graph?
We sometimes refer to a graph as a general graph to emphasize that the graph may have loops or multiple edges. The edges of a simple graph can be represented as a set of two element sets; for example, is a graph that can be pictured as in Figure .
What is a graph made up of?
A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called links or lines ). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically.
What are the edges of a simple graph?
The edges of a simple graph can be represented as a set of two element sets; for example, is a graph that can be pictured as in Figure . This graph is also a connected graph: each pair of vertices , is connected by a sequence of vertices and edges, , where and are the endpoints of edge .
Definitions in Graph Theory
Graph Theory has some unique vocabulary: 1. An arcis a directed line (a pair of ordered vertices). 2. An edge is line joining a pair of nodes. 2.1. Incident edges are edges which share a vertex. A edge and vertex are incidentif the edge connects the vertex to another. 3. A loopis an edge or arc that joins a vertex to itself. 4. A vertex, sometimes
More Definitions
An edge contractioninvolves removing an edge from a graph by merging the two vertices it used to join.In computer science and computer-based graph theory, a graph traversalis an exploration of a graph in which the vertices are visited or updated one by one.A Hamiltonian cycleis a closed loop where every node is visited exactly once. statisticshowto.com
Types of Graphs
An acyclic directed graphis a finite directed graph which has no directed cycles.A directed graphis a graph where the edges have direction; that is, they are ordered pairs of vertices.A condensationof a multigraph is the graph that results when you delete any multiple edges, leaving just one edge between any two points.If a graph has a path between every pair of vertices (there is no vertex not connected with an edge), the graph is called a connected graph. statisticshowto.com
Graph Theory in History
Graph Theory dates back to 1735 and Euler’s Seven Bridges of Königsberg. The city of Königsberg was a town with two islands, connected to each other and to the mainland by seven bridges. The question set was whether it were possible to take a walk and cross each bridge exactly once. In a first demonstration of graph theory, Euler showed that it was
Mantel’s Theorem
Mantel’s theorem, published in 1907, tells us the largest number of edges a graph with a given number of vertices may have without having a triangle for a subgraph. It can be stated as: A graph with n vertices and m edges will contain a triangle as a subgraph if and only if m > n2/4. statisticshowto.com
References
Introduction to Combinatorics and Graph Theory. Retrieved 8/11/2017 from: https://www.whitman.edu/mathematics/cgt_online/cgt.pdf Turan’s Theorem Mathematics of Bioinformatics statisticshowto.com
Introduction to Graph Theory Basics of Graph Theory Imp for GATE and UGC NET
Introduction to Graph Theory
Basic Concepts of Graph Theory in Discrete Mathematics
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Graph theory: basic definitions and theorems
GRAPH THEORY: BASIC DEFINITIONS AND THEOREMS 1 Definitions Definition 1 A graph G = (VE) consists of a set V of vertices (also called nodes) and |
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The first of these (Chapters 1-4) provides a basic foundation course containing definitions and examples of graphs connectedness Eulerian and Hamiltonian |
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1 Basic Definitions of Graph Theory
1 Basic Definitions of Graph Theory Definition 1 An undirected graph G = (VE) consists of a set V of elements called vertices and a |
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Parallel edges :- A more than one edge associated with a given pair of vertices such edges is called parallel edges for example edges e2 and e7 in Fig Types |
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Unit - IV GRAPH THEORY 11 Some Basic Definitions - R N College
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Basic Concepts in Graph Theory
Examples of graphs with loops appear in the exercises We have two definitions Definition 1 (simple graph) and Definition 2 (graph) How are they related? Let |
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1 Basic Definitions and Concepts in Graph Theory
CME 305: Discrete Mathematics and Algorithms 1 Basic Definitions and Concepts in Graph Theory A graph G(VE) is a set V of vertices and a set E of edges |
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Basic Concepts and Definitions of Graph Theory
As an example in Figure 1 2 two nodes n4 and n5 are adjacent Node n3 is incident with member m2 and m6 and deg (n2) = 4 1 2 3 ISOMORPHIC GRAPHS Two |
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Graph Theory - D-MATH
18 août 2016 · 1 Basic notions 1 1 Graphs Definition 1 1 A graph G is a pair G = (VE) where V is a set of vertices and E is a (multi)set |
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Graph Theory
As a matter of fact we can just as easily define a graph to be a diagram consist- ing of small circles called vertices and curves called edges where each |
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1 Basic Definitions of Graph Theory
1 Basic Definitions of Graph Theory Definition 1 An undirected graph G = (V,E) consists of a set V of elements called vertices, and a multiset E (repetition of |
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GRAPH THEORY: BASIC DEFINITIONS AND THEOREMS 1
A graph G = (V,E) consists of a set V of vertices (also called nodes) and a set E of edges Definition 2 If an edge connects to a vertex we say the edge is incident to |
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1 Basic Definitions and Concepts in Graph Theory - Stanford
Definition: A closed walk (circuit) on graph G(V,E) is an Eulerian circuit if it traverses each edge in E exactly once We call a graph Eulerian if it has an Eulerian |
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Basic Concepts and Definitions of Graph Theory
As an example, in Figure 1 2 two nodes n4 and n5 are adjacent Node n3 is incident with member m2 and m6, and deg (n2) = 4 1 2 3 ISOMORPHIC GRAPHS |
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GRAPH THEORY BASIC TERMINOLOGY PART I - cssiuedu
4 oct 2017 · Formal Definition: • A graph, G=(V, E), consists of two sets: • a finite non empty set of vertices(V), and • a finite set (E) of unordered pairs of |
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Basic Concepts in Graph Theory
Examples of graphs with loops appear in the exercises We have two definitions, Definition 1 (simple graph) and Definition 2 (graph) How are they related? Let G |
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Basic Concepts in Graph Theory - UCSD Mathematics
Examples of graphs with loops appear in the exercises We have two definitions, Definition 1 (simple graph) and Definition 2 (graph) How are they related? Let G |
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Graph Theory
In this section we will introduce a number of basic graph theory terms and concepts Study them carefully and pay special attention to the examples that are |
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Basic graph definitions
It would be convenient to say that there are two theories and two kinds of graphs: In the traditional definition of graphs, vertices are in a sense primary, and |
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Download Graph Theory Tutorial (PDF Version) - Tutorialspoint
Some examples for topologies are star, bridge, series, and parallel topologies graph theory stands up on some basic terms such as point, line, vertex, edge, |
