Degree sum adjacency polynomial of standard graphs and graph operations

Abstract

In this paper we explore the characteristic polynomials of degree sum adjacency matrix DSA(G) of a simple undirected graph G. We state a relation between the structure of a graph with the coefficients of its DSA polynomial. We obtain a generating function to find the number of walks of length k in a graph. Then, we obtain the degree sum adjacency polynomial for some standard graphs, derived graphs and for graph operations.

Keywords

• degree sum adjacency matrix, degree sum adjacency polynomial, number of walks.