IJPAM: Volume 101, No. 5 (2015)

TIGHT LOWER BOUND FOR LOCATING-TOTAL
DOMINATION NUMBER

R. Jayagopal$^1$, R. Sundara Rajan$^2$, Indra Rajasingh$^3$
$^{1,2,3}$School of Advanced Sciences
VIT University
Chennai, INDIA


Abstract. Locating-dominating set in a connected graph $G$ is a dominating set $S$ of $G$ such that for every pair of vertices $u$ and $v$ in $V(G) \setminus S$, $N(u)\cap S \neq N(v)\cap S$. Further, if $S$ is a total dominating set, then $S$ is called a locating-total dominating set. The locating-domination number $\gamma_{}^{L}(G)$ is the minimum cardinality of a locating-dominating set of $G$ and the locating-total domination number $\gamma_{t}^{L}(G)$ is the minimum cardinality of a locating-total dominating set of $G$. In this paper we prove that if $G$ is a necklace or a windmill graph, then $\gamma_{}^{L}(G) = \gamma_{t}^{L}(G)$.

Received: March 12, 2015

AMS Subject Classification: 05C69

Key Words and Phrases: dominating set, total dominating set, locating-dominating
set, locating-total dominating set, necklace, windmill graphs

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DOI: 10.12732/ijpam.v101i5.7 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 101
Issue: 5
Pages: 661 - 668


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