### 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

Walsh, Matthew, "THE HUB NUMBER OF A GRAPH", Int. J. Math. Comput. Sci 1, no. 1 (2006): 117-124.

Veettil, Ragi Puthan, and T. V. Ramakrishnan, "INTRODUCTION TO HUB POLYNOMIAL OF GRAPHS", Malaya Journal of Matematik (MJM) 8, no. 4, 2020 (2020): 1592-1596.

S. Alikhani and Y.H. Peng,"DOMINATING SETS AND DOMINATION POLYNOMIALS OF PATHS",International journal of Mathematics and mathematical sciences, 2009.

S. Alikhani and Y.H. Peng,"INTRODUCTION TO DOMINATION POLYNOMIAL OF A GRAPH ",arXiv preprint arXiv:0905.2251, 2009.

Sahib.Sh. Kahat, Abdul Jalil Khalaf and RoslanHasni,"DOMINATING SETS AND DOMINATION POLYNOMIALS OF WHEELS",Asian Journal of Applied Sciences(ISSN:2321- 0893),volume 02- Issue 03,June 2014.

Sahib.Sh. Kahat, Abdul Jalil M.Khalaf and RoslanHasni,"DOMINATING SETS AND DOMINATION POLYNOMIALS OF STARS",Australian Journal of Basics and Applied Science,8(6) June 2014,pp 383-386.

A.Vijayan,T.AnithaBaby,G.Edwin,"CONNECTED TOTAL DOMINATING SETS AND CONNECTED TOTAL DOMINATION POLYNOMIALS OF STARS AND WHEELS",IOSR Journal of Mathematics,VolumeII,pp 112-121.

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

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