Define bipartile graph with example. State the necessary conditions for the graphs to be isomorphic.

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Bipin Tiwari · Accepted Answer

A Bipartite Graph is a graph whose vertices can be divided into two independent sets, U and V such that every edge (u, v) either connects a vertex from U to V or a vertex from V to U. In other words, for every edge (u, v), either u belongs to U and v to V, or u belongs to V and v to U. We can also say that there is no edge that connects vertices of same set. Graph Isomorphism Conditions-   For any two graphs to be isomorphic, following 4 conditions must be satisfied-   Number of vertices in both the graphs must be same. Number of edges in both the graphs must be same. Degree sequence of both the graphs must be same. If a cycle of length k is formed by the vertices { v1 , v2 , ….. , vk } in one graph, then a cycle of same length k must be formed by the vertices { f(v1) , f(v2) , ….. , f(vk) } in the other graph as well.

Define bipartile graph with example. State the necessary conditions for the graphs to be isomorphic.

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Define bipartile graph with example. State the necessary conditions for the graphs to be isomorphic.

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