Minimum degree polynomial of graphs obtained by some graph operators

Abstract

Abstract: The minimum degree matrix MD(G) of a graph G of order n is an n× n symmetric matrix whose (i, j)th entry is min{di, dj} whenever i 6= j, and zero otherwise, where di and dj are the degrees of the ith and jth vertices of G, respectively. In the present work, we obtain the minimum degree polynomial of the graphs obtained by some graph operators (generalized xyz-point-line transformation graphs).