The energy of the Mycielskian of a regular graph

Let G be a finite connected simple graph and μ(G) be the Mycielskian of G. We show that for connected graphs G and H, μ(G) is isomorphic to μ(H) if and only if G is isomorphic to H. Furthermore, we determine the energy of the Mycielskian of a connected regular graph G in terms of the energy E(G) of G, where the energy of G is the sum of the absolute values of the eigenvalues of G. The energy of a graph has its origin in chemistry in that the energy of a conjugated hydrocarbon molecule computed using the Hückel theory in quantum chemistry coincides with the graph energy of the corresponding molecular graph. We show that if G is a regular graph of order n with E(G) > 3n, then μ(G) is hyperenergetic. 164 R. BALAKRISHNAN, T. KAVASKAR AND W. SO Figure 1: μ(K1,3 + e)