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Non-split and Inverse Non-split Domination Numbers in the Join and Corona of Graphs
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 60 - Number 2 |
| Year of Publication: 2012 |
| Authors: Esamel M. Paluga, Rolando N. Paluga |
10.5120/9661-4082
|
Esamel M. Paluga, Rolando N. Paluga . Non-split and Inverse Non-split Domination Numbers in the Join and Corona of Graphs. International Journal of Computer Applications. 60, 2 ( December 2012), 1-5. DOI=10.5120/9661-4082
Abstract
A dominating set D of a graph G = (V;E) is non-split dominating set if hV n Di is connected. The non-split domination number of G is the minimum cardinality of a non-split dominating set inG. LetD be a minimum dominating set inG. If a subset D 0 of V n D is dominating in G, then D 0 is called an inverse dominating set with respect to D. Furthermore, if V n D 0 is connected, then D 0 is called an inverse non-split dominating set. The inverse non-split domination number of G is the minimum cardinality of an inverse non-split dominating set in G. In this paper, characterization of non-split dominating sets in the join and corona of two graphs are presented. Furthermore, explicit formulas for determining the non-split and inverse nonsplit domination numbers of these graphs are also determined.
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