Multiple Intruder Locating Dominating Sets

K. Venugopal¹ , K. A. Vidya²

Section:Research Paper, Product Type: Isroset-Journal
Vol.6 , Issue.2 , pp.394-398, Apr-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.394398

Online published on Apr 30, 2019

Copyright © K. Venugopal, K. A. Vidya . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
Safeguarding of facilities has been at a major focus in graph theoretical research which has led to a surge of various parameters of locating dominating sets in graphs. However, in all those parameters, a single intruder is assumed to be present in a network. In this paper, we introduce Multiple Intruder Locating Dominating (MILD) sets where one is interested in finding the presence as well as the locations of intruders at multiple (possibly all) locations in a network. The number of vertices in the smallest MILD set of a graph G is called its MILD number, denoted by MILD(G). For a simple connected graph of order n, the MILD number lies between n/2 and n-1, both inclusive. The graphs which attain these bounds are characterized.

Key-Words / Index Term :
Domination, Locating Domination, Multiple intruder locating domination

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