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

#### Abstract

*G*denoted 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

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DOI: http://dx.doi.org/10.23755/rm.v44i0.886

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