The isomorphism graph can be described as a graph in which a single graph can have more than one form. That means two different graphs can have the same number of edges, vertices, and same edges connectivity. These types of graphs are known as isomorphism graphs.
The example of an isomorphism graph is described as follows:
In above figure, The same graph is represented in more than one form.
Number of vertices of graph (a) must be equal to graph (b), i.e., one to one correspondence some goes for edges.
» Conditions for graph isomorphism
Any two graphs will be known as isomorphism if they satisfy the following four conditions:
- There will be an equal number of vertices in the given graphs.
- There will be an equal number of edges in the given graphs.
- There will be an equal amount of degree sequence in the given graphs.
- If the first graph is forming a cycle of length k with the help of vertices {v1, v2, v3, …. vk}, then another graph must also form the same cycle of the same length k with the help of vertices {v1, v2, v3, …. vk}.
