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

DOI:

10.18052/www.scipress.com/BMSA.9.27

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:

Aug 2014

Authors:

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License

References:

J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (American Elsevier, New York, 1977).

G. Chartant and L. Lesniak, Graphs & Digraphs (Wadsworth and Brooks/cole, Monterey, CA, third edition, 1996).

F. Harary, Graph theory (Addison-Wesley, Reading, MA, 1969).

T.W. Haynes, S.T. Hedetniemi and P.J. Slater Fundamentals of Domonation in Graphs (Marcel dekker, Inc., New York, 1998).

T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domonation in Graphs Advanced topics (Marcel dekker, Inc., New York, 1998).

D.B. West, Introduction to Graph Theory (Prentice Hall, New Jersey, 1996).