Research Article
Global Domination Upon Edge Addition Stable Graphs
|
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
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| Volume 43 - Issue 19 |
| Published: April 2012 |
| Authors: K. Kavitha, N. G. David |
10.5120/6211-8859
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K. Kavitha, N. G. David . Global Domination Upon Edge Addition Stable Graphs. International Journal of Computer Applications. 43, 19 (April 2012), 25-27. DOI=10.5120/6211-8859
@article{ 10.5120/6211-8859,
author = { K. Kavitha,N. G. David },
title = { Global Domination Upon Edge Addition Stable Graphs },
journal = { International Journal of Computer Applications },
year = { 2012 },
volume = { 43 },
number = { 19 },
pages = { 25-27 },
doi = { 10.5120/6211-8859 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2012
%A K. Kavitha
%A N. G. David
%T Global Domination Upon Edge Addition Stable Graphs%T
%J International Journal of Computer Applications
%V 43
%N 19
%P 25-27
%R 10.5120/6211-8859
%I Foundation of Computer Science (FCS), NY, USA
Abstract
Let G be a simple, finite and connected graph. A dominating set D of a graph G is a global dominating set if D is also a dominating set of . The global domination number is the minimum cardinality of a minimal global dominating set of G. A graph is global domination edge critical if addition of any arbitrary edge changes the global domination number. On the other hand, a graph is global domination edge stable if addition of any arbitrary edge has no effect on the global domination number. In this paper, we study the concepts of global domination and connected global domination upon edge addition stable property for cycle and path graphs. We determine sharp bounds on the global domination and connected global domination number of global domination, total global domination and connected global domination edge addition stable graphs.
References
- D. Hanson, P. Wang, A note on extremal total domination edge critical graphs, Util. Math. 63(2003) 89 – 96.
- F. Harary, Graph Theory, Narosa Publishing, Bombay, 1969.
- S. T. Hedetniemi and R. C. Laskar, Topics in Domination, Elsevier Science Publishers B. V. , Netherlands, 1991.
- V. R. Kulli and B. Janakiram, The Total Global Domination Number of a Graph, Indian J. Pure appl. Math. , 27(6) : 537 – 542, June 1996.
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