Results on Neighborhoods sets Polynomial of a graph

J.Joseline Manora a,* and I.Paulraj Jayasimmanb

Results on Neighborhoods sets Polynomial of a graph

Authors :

J.Joseline Manora ^a,* and I.Paulraj Jayasimman^b

Author Address :

^aDepartment of Mathematics, T.B.M.L College, Porayar-609307, India.
^bDepartment of Mathematics, Indira Institute of Engineering and Technology, Thiruvallur-631203, India.

*Corresponding author.

Abstract :

The neighborhood set polynomial$N\left(G,x\right)$ of a graph $G$ of order $n$ is defined as $N\left(G,x\right) = \sum \limits_{i=n_0(G)}^{\left|V(G)\right|}$ ,where $n_0(G)$ is the neighborhood number of a graph $G$. The neighborhood number of a graph G was introduced by E.Sampathkumar et.al. [6]. The $N\left(G,i\right)$ be the family of neighborhood sets with cardinality i. $n_i\left(G,i\right)=\left|N(G,i)\right|$.For this neighborhood number neighborhood sets polynomial of $G$ is defined and studied for some standard graphs.