Results on Neighborhoods sets Polynomial of a graph
Authors :
J.Joseline Manora a,* and I.Paulraj Jayasimmanb
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.
Keywords :
Neighborhood Polynomial.
DOI :
Article Info :
Received : July 10, 2015; Accepted : August 29, 2015.