Connected 2- Dominating Sets and Connected 2- Domination Polynomials of the Complete Bipartite Graph k_(2,m)

Authors

  • Y.A. Shiny Reg. No.: 19213042092006, Research Scholar (Full time), Research Department of Mathematics, Women’s Christian College, Nagercoil. Affiliated by Manonmaniam Sundaranar University, Tamil Nadu,
  • Anithababy T Assistant Professor, Research Department of Mathematics, Women’s Christian College, Nagercoil. Affiliated by Manonmaniam Sundaranar University, Tamil Nadu,

DOI:

https://doi.org/10.23755/rm.v44i0.889

Keywords:

Dominating, Connected and cardinality

Abstract

Let  be a simple graph.Let  be the family of connected 2 dominating sets in with cardinality  and |.Then the polynomial is called the 2 domination polynomial of  where is the connected 2  domination number of Let  be the family of connected 2 dominating sets of theComplete bipartite graph  with cardinality  and let .Then the connected 2  domination polynomial   of  is defined as where  is the connected2 – domination number of .In this paper, we obtain a recursive formula for .Using this recursive formula, we construct the connected 2 domination polynomial  is the number of connected 2 dominating sets of  of cardinality  and some properties of this polynomial have been studied

References

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A.Vijayan,T.Anithababy,G.Edwin, “Connected Total Dominating Sets andConnected Total Domination Polynomials of Fan Graphs F_(2,n) ".InternationalJournal of Mathematical Sciences and Engineering Applications(IJMSEA),Vol.10, No.1(April 2016), pp.135-146, ISSN:0473-9424.

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Published

2022-12-11

Issue

Vol. 44 (2022): Special Issue: Recent Trends in Mathematics and its Applications

Section

Volume 45-2023

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