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? (i.e., graph isomorphism) The graphs in question may be expressed differently in terms of graph equations.What are the graphs (solutions) G and H such that the line graph of G is same as the total graph of H? (What are G and H such that L(G) = T(H) ?).For example, G = K3, and H = K2 are the solutions of the graph equation L(K3) = T(K2) and G = K4, and H = K3 are the solutions of the graph equation L(K4) = T(K3).Note that T(K3) is a 4-regular graph on 6 vertices.
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