Degree sum adjacency polynomial of standard graphs and graph operations

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


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.


Degree sum adjacency matrix, Degree sum adjacency polynomial, Number of walks.

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C. Adiga, M. Smitha, On maximum degree energy of a graph, Int. J. Contemp. Math. Sci, 4, (2009), 385--396.

R. B. Bapat, Graphs and Matrices, Springer, 2010.

D. M. Cvetkovi'c, M. Doob,and H. Sachs. Spectra of Graphs Theory and Applications, Academic Press, New York, 1980.

F. Harary, Graph Theory, Addison-Wesley, Reading, 1969.

H. Minc, M. Marcus, A Survey of Matrix Theory and Matrix Inequalities, Prindle, Weber Schmidt, Boston, 1964.

H. S. Ramane, D. S. Revenkar, J. B. Patil, Bounds for the Degree sum eigenvalue and Degree sum energy of a graph, Int. J. Pure App. Sci., 6(2), (2013), 161--167.

H. S. Ramane and S. S. Shinde, Degree exponent polynomial and degree exponent energy of graphs, Indian J. Discrete Math., 2(1) (2016),01 -- 07.

H. S. Ramane and S. S. Shinde, Degree exponent polynomial of graphs obtained by some graph operations, Electronic Notes in Discrete Math., 63 (2017), 161--168.

H. S. Ramane, K. C. Nandeesh, G. A. Gudodagi, B. Zhou, Degree subtraction eigenvalues and energy of graphs, Computer Science Journal of Moldova, 26(2), (2018).

R. K. Zaferani, A study of some topics in the theory of graphs, (Ph.D. Thesis), University of Mysore, Mysore, 2009.


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