Degree sum adjacency polynomial of standard graphs and graph operations

S S Shinde (KLE Technological University)
H S Ramane (bDepartment of Mathematics, Karnatak University, Dharwad - 580003, India)
S B Gudimani (Depathment of Mathematics, KLE Technological University, Hubballi-580031, India)
N Swamy (Depathment of Mathematics, KLE Technological University, Hubballi-580031, India)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 10, No 1 (2022): Electronic Journal of Graph Theory and Applications

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.