• ON GEODETIC POLYNOMIAL OF GRAPHS WITH EXTREME VERTICES

Abstract

Let G=(V,E) be a simple graph. A set of vertices S of a graph G is geodetic, if every vertex of G lies on a shortest path between two vertices in S. The geodetic number of G is the minimum cardinality of all geodetic sets of G, and is denoted by g(G). In [10], the concept of geodetic polynomial is defined as where is the number of geodetic sets of G with cardinality i. In this paper, we obtain the geodetic polynomials of the helm graph. Also, we compute the polynomials for some specific graphs.