DOMINATION POLYNOMIALS OF THE JEWEL GRAPH AND ITS COMPLEMENT

Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 36

Abstract

Let $G=(V(G),E(G))$ be a simple graph. The Jewel graph $J_n$ is a graph with vertex set $V(J_n)=\{u,v,x,y,u_i : 1\leq i\leq n\}$ and edge set $E(J_n)=\{ux,uy,xy,xv,yv,uu_i,vu_i :1\leq i\leq n\}$. The domination polynomial of a graph $G$ of order $n$ is the polynomial $D(G,x)=\sum_{i=\gamma(G)}^n d(G,i)x^i$, where $d(G,i)$ is the number of dominating sets of $G$ of cardinality $i$. In this paper, we present various domination polynomials of the Jewel graph $J_n$. Also we determine the same results for the complement of the Jewel graph.

Keywords and Phrases

Domination polynomial, Jewel graph.

A.M.S. subject classification

05C31, 05C69.

.....

Download PDF 36 Click here to Subscribe now