Equalityof Secure Domination and Inverse Secure Domination Numbers
ABSTRACT:
Let G = (V, E) be a graph. Let D be a minimum secure dominating set of G. If V – D contains a secure total dominating set D’ of G, then D’ is called an inverse secure dominating set with respect to D. The smallest cardinality of inverse secure dominating set of G is the secure domination number s -1(G) of G. In this paper, we obtain some graphs for which s(G) = s -1(G) and establish some results on this respect. Also we obtain some graphs for which s(G) =s -1(G) = 2 . p where p is the number of vertices of G.
KEYWORDS: dominating set, secure dominating set, inverse secure dominating set, inverse secure domination number.. Mathematics Subject Classification: 05C69, 05C78
- DOI:
http://dx.doi.org/10.22147/jusps-A/280601
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Let G = (V, E) be a graph. Let D be a minimum secure dominating set of G. If V – D contains a secure total dominating set D’...