Stability of Complement Degree Polynomial of Graphs

Main Article Content

Safeera K
Anil Kumar V


     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


Download data is not yet available.

Article Details

How to Cite
K S, V AK. Stability of Complement Degree Polynomial of Graphs. Baghdad Sci.J [Internet]. 2023 Mar. 1 [cited 2023 Mar. 21];20(1(SI):0300. Available from:


Omran AA, Oda HH. Hn-Domination in Graphs. Baghdad Sci J. 2019; 16(1): 242-247.

Safeera K, Kumar VA. Vertex cut polynomial of graphs. Adv Appl Discrete Math. 2022; 32(1): 1-12.

Juma ARS, Abdulhussain MS, Al-khafaji SN. Faber Polynomial Coefficient Estimates for Subclass of Analytic Bi-Bazilevic Functions Defined by Differential Operator. Baghdad Sci J. 2019; 16(1(Suppl.)): 248-253.

Shikhi M, Kumar AV. On the stability of common neighbor polynomial of some graphs. South East Asian J Math. Math Sci. 2018; 14(1): 95-102.

Fuhrmann PA. A polynomial approach to linear algebra. Springer-Berlin Heidelberg. New York; 1996. 422 p.