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Global Domination Upon Edge Addition Stable Graphs

by K. Kavitha, N. G. David
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 43 - Number 19
Year of Publication: 2012
Authors: K. Kavitha, N. G. David
10.5120/6211-8859

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 },
issue_date = { April 2012 },
volume = { 43 },
number = { 19 },
month = { April },
year = { 2012 },
issn = { 0975-8887 },
pages = { 25-27 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume43/number19/6211-8859/ },
doi = { 10.5120/6211-8859 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:33:49.682684+05:30
%A K. Kavitha
%A N. G. David
%T Global Domination Upon Edge Addition Stable Graphs
%J International Journal of Computer Applications
%@ 0975-8887
%V 43
%N 19
%P 25-27
%D 2012
%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
  1. D. Hanson, P. Wang, A note on extremal total domination edge critical graphs, Util. Math. 63(2003) 89 – 96.
  2. F. Harary, Graph Theory, Narosa Publishing, Bombay, 1969.
  3. S. T. Hedetniemi and R. C. Laskar, Topics in Domination, Elsevier Science Publishers B. V. , Netherlands, 1991.
  4. 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.
Index Terms

Computer Science
Information Sciences

Keywords

Domination Global Domination Connected Global Domination Edge Addition Stable

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