Maximum and minimum degree energies of p-splitting and p-shadow graphs

Abstract

Let vi and vj be two vertices of a graph G. The maximum degree matrix of G is given in [2] by dij = {max {di, dj} if vi and vj are adjacent 0 otherwise. Similarly the (i, j)-th entry of the minimum degree matrix is defined by taking the minimum degree instead of the maximum degree above, [1]. In this paper, we have elucidated a relation between maximum degree energy of p−shadow graphs with the maximum degree energy of its underlying graph. Similarly, a relation has been derived for minimum degree energy also. We disprove the results EM(S0 (G)) = 2EM(G) and Em(S0 (G)) = 2Em(G) given by Zheng-Qing Chu et al. [3] by giving some counterexamples.