Degree sum adjacency polynomial of standard graphs and graph operations

S S Shinde, H S Ramane, S B Gudimani, N Swamy

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.

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DOI: http://dx.doi.org/10.5614/ejgta.2022.10.1.2

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