The present paper is focusing on the connection between the Isomorphic groups and the Isomorphic graphs. We established a few results on the necessary and sufficient condition on the dimension of the graphs, which are isomorphic with respect to the isomorphic groups. We proved those results depending on the Isomorphic groups. We discussed the methods to find isomorphic graphs by using isomorphic groups. We derived few results on the isomorphism of graphs, by illustrating few examples.
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