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 (i.e., graph isomorphism)? The graphs in question may be expressed differently in terms of graph equations. K 2 {displaystyle K_{2}} K 3 {displaystyle K_{3}} K 4 {displaystyle K_{4}} 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.