Connected Hub Sets and Connected Hub Polynomials of the Lollipop Graph L_(p,1)

Abstract

Let be a graph with vertex set . The number of vertices in is the order of and is denoted by . The connected hub polynomial of Gdenoted by is defined as where denotes the number of connected hub sets of of cardinality and denotes the connected hub number of .Let denotes the Lollipop graph with vertices. The connected hub polynomial of denoted by is defined as,where denotes the number of connected hub sets of of cardinality , and denotes the connected hub number of .In this paper, we derive a recursive formula for . From this recursive formula, we construct the connected hub polynomial of as,Also we study some properties of this polynomial

Keywords

• lollipop graph, connected hub set, connected hub number, connected hub polynomial