MAXIMUM AND MINIMUM DEGREE ENERGIES OF p-SPLITTING AND p-SHADOW GRAPHS

MAXIMUM AND MINIMUM DEGREE ENERGIES OF p-SPLITTING AND p-SHADOW GRAPHS

K. S. Rao, K. Saravanan, K. N. Prakasha, I. N. Cangul

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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 fdi; djg if vi and vj are adjacent 0 otherwise: Similarly the (i; j)-th entry of the minimum degree matrix is de ned 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 pshadow 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 counterexam- ples.

Keywords

maximum degree energy, minimum degree energy, splitting graph, shadow graph.