Various graphs has been defined on groups in the literature and the relation between the algebraic properties and graph theoretic properties has been studied extensively. The main goal of this project is to study the inter-relationship between the group properties and graph theoretic properties, i.e., if two graphs on two groups are isomorphic, are the groups isomorphic? If not, what is the next best thing that we can say about these groups? Or are there any additional conditions, under which the groups are isomorphic?
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