Vol. 7(2) July 2019, No. 21, pp. 230-243.

MINIMUM DEGREE ENERGY OF GRAPHS
Vol. 7(2) July 2019, No. 21, pp. 230-243
B. BASAVANAGOUD AND PRAVEEN JAKKANNAVAR

Abstract

Let G be a graph of order n. Then an n × n symmetric matrix is called the minimum degree matrix MD(G) of a graph G, if its (i, j) th entry is min{di, dj} whenever i 6= j, and zero otherwise, where di and dj are the degrees of i th and j th vertices of G, respectively. In the present work, we obtain the characteristic polynomial of the minimum degree matrix of graphs obtained by some graph operations. In addition, bounds for the largest minimum degree eigenvalue and minimum degree energy of graphs are obtained.


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