Degree Sum Adjacency Energy and Energy of Some Special Graphs

Abstract

A Degree sum adjacency matrix of graph $G$ is defined as the addition of degrees of vertices if both are adjacent and 0 otherwise. The Degree sum adjacency eigenvalues of the graph are the eigenvalues of the Degree sum adjacency matrix of the graph and an absolute sum of the Degree sum adjacency eigenvalues is called Degree sum adjacency energy of the graph. Splitting graph, m-Splitting graph, Shadow graph and m-Shadow graph are obtained by graph operation on the given graph. In this paper, we found a relation between Degree sum adjacency energy of the k-regular graph and Degree sum adjacency energy of its Splitting graph and m-Splitting graph. In addition, we found Degree sum adjacency energy of the Shadow graph and m-Shadow graph of the connected graph in the form of a Degree sum adjacency energy of the graph