On Real Roots of Complement Degree Polynomial of Graphs.

Abstract

Let  G=(V,E) be a simple undirected graph of order  xⁱ n and let CD(G,i) be the set of vertices of degree i in complement graph  and let Cd_i(G)=|CD(G,i)|. Then complement degree polynomial of G is defined as CD[G,x]=$\sum_{i=\delta(\overline{G})}^{\Delta(\overline{G})}$Cd_i(G)xⁱ. In this paper, focus on real roots of complement degree polynomial of graphs and bounds of roots of complement degree polynomial of graphs.