TY - JOUR
T1 - Locating Equitable Domination and Independence Subdivision Numbers of Graphs
AU - Sumathi, P.
AU - Alarmelumangai, G.
JF - Bulletin of Mathematical Sciences and Applications
VL - 9
SP - 27
EP - 32
SN - 2278-9634
PY - 2014
PB - SciPress Ltd
DO - 10.18052/www.scipress.com/BMSA.9.27
UR - https://www.scipress.com/BMSA.9.27
KW - Independence
KW - Locating Equitable Domination
KW - Subdivision Numbers
AB - 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 sdγle(G). The independence subdivision number sdβle(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 sdγle(G) and sdβle(G) for some families of graphs.
ER -