Private Dominating Sets and Private Domination Polynomial of Friendship Graphs

AngelinKavithaRaj S¹ , SenthilMurugan P²

Section:Research Paper, Product Type: Isroset-Journal
Vol.6 , Issue.3 , pp.41-44, Jun-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i3.4144

Online published on Jun 30, 2019

Copyright © AngelinKavithaRaj S , SenthilMurugan P . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
Let G be a simple graph of order n and V denotes vertex set and E denotes edge set of G. A subset S of V is called Private domination set of graph G if it is dominating set and also every u in S there exist an external private neighbour v in other than S in V. And Private Domination Polynomial of G is the polynomial denoted as PD(G,x)) , is the sum of Private dominating sets Pd(G,j), where Pd(G,j) be the cardinality of the family of Private domination set with cardinality j . Let m be any positive integer and Fm be the Friendship graph constructed by joining K1 and m times of K2. In this paper, we investigate the properties of Private domination set and Private Domination Polynomial for family of Friendship graph and a special case called Friendship graph with missing vertex.

Key-Words / Index Term :
Dominating set, Domination Polynomial, Private Domination set, Private Domination Polynomial, Friendship Graph, Missingvertex

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