VERTEX COVER POLYNOMIAL OF SEA URCHIN GRAPH AND LOLLY POP GRAPH

Abstract

The vertex cover polynomial of a graph G of order n has been already introduced in [3].  it is defined as the polynomial, C (G, x) = c (G, i)xi , where c (G , i) is the number of vertex covering sets of  G  of size i and _áµ(G) is the  covering number of G.  In this paper we have established a general formula for finding the vertex Cover Polynomial of Sea Urchin graph, Lolly Pop graph. The coefficients. of the polynomial satisfies some identities.  Also we proved that the coefficient of the vertex cover, polynomial  is log-Concave

key words : Vertex covering set, Vertex covering number, Vertex cover polynomial.