IJPAM: Volume 101, No. 5 (2015)

ETERNAL SECURITY IN MYCIELSKIAN GRAPHS

P. Roushini Leely Pushpam$^1$, G. Navamani$^2$
$^1$Department of Mathematics
D.B. Jain College
Chennai 600 097, Tamil Nadu, INDIA
$^2$Department of Mathematics
Kumararani Meena Muthiah College of Arts and Science
Chennai 600 020, Tamil Nadu, INDIA


Abstract. An eternal $m$-security number $\sigma_m(G)$ of a graph $G=(V,E)$ is defined as the minimum number of guards to handle an arbitrary sequence of single attacks using multiple-guard shifts. A suitable placement of the guard is called an eternal $m$-secure set. In this paper we find the values of this parameter for Mycielskian graphs of complete graphs, paths, cycles, complete bipartite graphs and wheels.

Received: March 12, 2015

AMS Subject Classification: 05C69

Key Words and Phrases: eternal security, domination number, Mycielskian graphs

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DOI: 10.12732/ijpam.v101i5.5 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: 641 - 649


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