Graphs | Types of Graphs

All definition of graphs. Finite graph, Infinite graph, Undirected graph, Directed graph, Mixed graph, Simple graph, Multigraph,
Psuedograph, Complete Graph, Regular Graph, Cubic graph, Cyclic Graph, Wheel graph, Weighted graph, Bipartite graph, Complete Bipartite Graph

1. Topic: Different types of graphs Page 1

2. Definition of graph: Graphs are discrete structures consisting of vertices and edges that connect these vertices. There are different kinds of graphs, depending on whether edges have directions, whether multiple edges can connect the same pair of vertices, and whether loops are allowed, whether weight of edges are given, etc. Page 2

3. Types of graph 1. Finite graph: A  finite graph is a graph in which the vertex set and the edge set are finite sets . 2. Infinite graph : A  infinite graph is a graph in which the vertex set and the edge set are  infinite sets . Page 3

4. 3. Undirected graph: An undirected graph is a graph in which edges have no orientation. 4. Directed graph: A directed graph is a graph in which edges have orientations. 5. Mixed graph: A mixed graph is a graph in which some edges may be directed and some may be undirected . Page 4

5. 6. Simple graph: A simple graph is an undirected graph without multiple edges or loops. 7. Multigraph : Multiple edges are two or more edges that connect the same two vertices. A loop is an edge that connects a vertex to itself. 8. Psuedograph :A graph in which loops and multiple edges are allowed is called psuedograph . Page 5

6. 9. Complete Graph- A simple graph G is said to be complete if every vertex in G is connected with every other vertex . 10. Regular Graph- A graph in which all the vertices are of equal degree is called a regular graph . Page 6

7. 11. Cubic graph: Cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular  graph. 12.Cyclic Graph: A graph with continuous sequence of vertices and edges is called a cyclic graph. 13. Wheel graph: A wheel graph is a graph formed by connecting a single universal vertex to all vertices of a cycle . Page 7

8. 14. Weighted graph: A weighted graph is a graph in which a number (the weight) is assigned to each edge . 15. Bipartite graph: A   bipartite graph  is a graph in which the vertex set can be partitioned into two sets. 16. Complete Bipartite Graph: A complete bipartite graph is a bipartite graph in which each vertex in the first set is joined to every single vertex in the second set . Page 8

9. That’s all Thank you Page 9