Liar’s domination in graphs under some operations

Authors

  • Sergio Jr. Rosales Canoy
  • Carlito Bancoyo Balandra

DOI:

https://doi.org/10.5556/j.tkjm.48.2017.2188

Keywords:

liar's dominating set, liar's-domination number, join, corona, lexicographic product

Abstract

A set $S\subseteq V(G)$ is a liar's dominating set ($lds$) of graph $G$ if $|N_G[v]\cap S|\geq 2$ for every $v\in V(G)$ and $|(N_G[u]\cup N_G[v])\cap S|\geq 3$ for any two distinct vertices $u,v \in V(G)$. The liar's domination number of $G$, denoted by $\gamma_{LR}(G)$, is the smallest cardinality of a liar's dominating set of $G$. In this paper we study the concept of liar's domination in the join, corona, and lexicographic product of graphs.

Author Biographies

Sergio Jr. Rosales Canoy

Department ofMathematics and Statistics, College of Science andMathematics,MSU-Iligan Institute of Technology, 9200 Iligan City, Philippines.

Carlito Bancoyo Balandra

Department ofMathematics and Statistics, College of Science andMathematics,MSU-Iligan Institute of Technology, 9200 Iligan City, Philippines.

References

T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of Domination in Graphs,

Monographs and textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 208(1998).

M. Nikodem, False alarm in fault-tolerant dominating sets in graphs, Opuscula Mathematica, 32(2012), 751--760.

P. J. Slater, Liar's domination, Networks, 54(2009), 70--74.

P. J. Slater and M. L. Roden, Liar's domination in graphs, Discrete Mathematics, 309(2008), 5884--5890.

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Published

2017-03-30

How to Cite

Canoy, S. J. R., & Balandra, C. B. (2017). Liar’s domination in graphs under some operations. Tamkang Journal of Mathematics, 48(1), 61–71. https://doi.org/10.5556/j.tkjm.48.2017.2188

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Section

Papers