Graph equation


In graph theory, Graph equations are equations in which the unknowns are graphs. One of the central questions of graph theory concerns the notion of isomorphism. We ask: When are two graphs the same ? The graphs in question may be expressed differently in terms of graph equations.
What are the graphs G and H such that the line graph of G is same as the total graph of H? = T.
For example, G = K3, and H = K2 are the solutions of the graph equation L = T and G = K4, and H = K3 are the solutions of the graph equation L = T.
Note that T is a 4-regular graph on 6 vertices.

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