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

T Anggelinshiny, Baby Anitha

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

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References


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

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Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.