Graph equation

Article summary

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 = K 3 , and H = K 2 are the solutions of the graph equation L(K 3 ) = T(K 2 ) and G = K 4 , and H = K 3 are the solutions of the graph equation L(K 4 ) = T(K 3 ). Image: Complete graph K2.svg|::: K_2 Image: Complete graph K3.svg|::: K_3 Image: Complete graph K4.svg|::: K_4 Note that T(K 3 ) is a 4-regular graph on 6 vertices.

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