Characterization of non-isomorphic graphs but isomorphic total graphs?

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Sunilkumar M Hosamani

Dear Sriram Vaidyanathan,

Since G is an induced subgraph of total graph therefore if two graphs G and H are isomorphic then their total graphs are isomorphic.

Roumen Nedev

One criteria may be the vertex degree. For example, for big graphs, one can estimate the average degree of the vertices of G, and compare it the same number on H.

Regards