Graph and Tree part 2

University: Babu Banarasi Das University

Course: Graph Theory (BSM 1654)

7 Documents

Students shared 7 documents in this course

1. Null Graph: A null graph is defined as a graph which consists only the isolated vertices.

Example: The graph shown in fig is a null graph, and the vertices are isolated vertices.

2. Undirected Graphs: An Undirected graph G consists of a set of vertices, V and a set of edge E.

The edge set contains the unordered pair of vertices. If (u, v)∈E then we say u and v are connected by

an edge where u and v are vertices in the set V.

Example: Let V = {1, 2, 3, 4} and E = {(1, 2), (1, 4), (3, 4), (2, 3)}.Draw the graph.HTML Tutorial

Solution: The graph can be drawn in several ways.

Two of which are as follows:

3. Multigraph: If in a graph multiple edges between the same set of vertices are allowed, it is known

as Multigraph. In other words, it is a graph having at least one loop or multiple edges.

4. Directed Graphs: A directed graph or digraph G is defined as an unordered pair (V, E), where V is

the set of points called vertices and E is the set of edges. Each edge in the graph G is assigned a

direction and is identified with an ordered pair (u, v), where u is the initial vertex, and v is the end

vertex.