Product Signed Domination in Graphs

Authors

  • T M Velammal
  • A Nagarajan
  • K Palani Associate Professor,A.P.C. Mahalaxmi College For Women, Thoothukudi-628002

DOI:

https://doi.org/10.23755/rm.v44i0.923

Keywords:

graphs, product signed dominating function, product signed domination number

Abstract

Let  be a simple graph. The closed neighborhood of , denoted by , is the set . A function  is a product signed dominating function, if for every vertex where . The weight of , denoted by , is the sum of the function values of all the vertices in . . The product signed domination number of  is the minimum positive weight of a product signed dominating function. In this paper, we establish bounds on the product signed domination number and estimate product signed domination number for some standard graphs

References

J. Dunbar, S.T. Hedetniemi. Henning, and P.J. Slater (1995), Signed Domination in Graph Theory, In: Graph Theory, Combinatorics and Applications, John Wiley & Sons, New York, 311-322.

Ernest J. Cockayneand Christina M. Mynhardt (1996), On AGeneralisation Of Signed Dominating Funtions Of Graphs,ArsCombinatoria, 43, 235-245.

S.M. Hosseini Moghaddam (2015), New Bounds On The Signed Domination Numbers Of Graphs, Australasian Journal Of Combinatorics, 61(3), 273-280

IzakBroere, Johannes H. Hattingh, Michael A. Henning, and Alice A. McRae (1995), Majority Domiation In Graphs, Discrete Mathematics, 138, 125-135.https://doi.org/10.1016/0012-365X(94)00194-N

Odile Favaron (1996), Signed Domination In Regular Graphs, Discrete Mathematics, 158, 287-293.https://doi.org/10.1016/001-365X(96)00026-X

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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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