Let G = (V,E) be a simple, undirected, finite nontrivial graph. A non empty set DV of vertices in a graph G is a dominating set if every vertex in V-D is adjacent to some vertex in D. The domination number (G) is the minimum cardinality of a dominating set of G. A dominating set D is a locating equitable dominating set of G if for any two vertices u,wєV-D, N(u)∩D ≠ N(w)∩D, |N(u)∩D| ≠ |N(w)∩D|. The locating equitable domination number of G is the minimum cardinality of a locating equitable dominating set of G. The locating equitable domination subdivision number of G is the minimum number of edges that must be subdivided (where each edge in G can be subdivided at most once) in order to increase the locating equitable domination number and is denoted by sdγ_{le}(G). The independence subdivision number sdβ_{le}(G) to equal the minimum number of edges that must be subdivided in order to increase the independence number. In this paper, we establish bounds on sdγ_{le}(G) and sdβ_{le}(G) for some families of graphs.

Periodical:

Bulletin of Mathematical Sciences and Applications (Volume 9)

Pages:

27-32

Citation:

P. Sumathi and G. Alarmelumangai, "Locating Equitable Domination and Independence Subdivision Numbers of Graphs", Bulletin of Mathematical Sciences and Applications, Vol. 9, pp. 27-32, 2014

Online since:

August 2014

Authors:

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License

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Cited By:

[1] A. Kelarev, W. Susilo, M. Miller, J. Ryan, "Ideals of Largest Weight in Constructions Based on Directed Graphs", Bulletin of Mathematical Sciences and Applications, Vol. 15, p. 8, 2016

DOI: https://doi.org/10.18052/www.scipress.com/BMSA.15.8