Stability of Complement Degree Polynomial of Graphs

Abstract

A graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense related. The objects correspond to mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line). A directed graph is a graph in which edges have orientation. A simple graph is a graph that does not have more than one edge between any two vertices and no edge starts and ends at the same vertex. For a simple undirected graph G with order n, and let denotes its complement. Let δ(G), ∆(G) denotes the minimum degree and maximum degree of G respectively. The complement degree polynomial of G is the polynomial CD[G,x]= , where Cdi(G) is the cardinality of the set of vertices of degree i in . A multivariable polynomial f(x1,...,xn) with real coefficients is called stable if all of its roots lie in the open left half plane. In this paper, investigate the stability of complement degree polynomial of some graphs. 2020 Mathematics Subject Classification: 05C31, 05C50

Keywords

• Complement degree polynomial, Complement of a graph, Degree of a vertex, Graph polynomial, Root of polynomial, Stability of polynomial