Degree Subtraction Adjacency Polynomial and Energy of Graphs obtained from Complete Graph

Abstract

The degree subtraction adjacency matrix of a graph G is a square matrix DSA(G)=[dij], in which dij=d(vi)-d(vj), if the vertices vi and vj are adjacent and dij=0, otherwise, where d(u) is the degree of a vertex u. The DSA energy of a graph is the sum of the absolute values of the eigenvalues of DSA matrix. In this paper, we obtain the characteristic polynomial of the DSA matrix of graphs obtained from the complete graph. Further we study the DSA energy of these graphs.