Equalityof Secure Domination and Inverse Secure Domination Numbers

AUTHOR AND
AFFILIATION

V.R. KULLI
Department of Mathematics, Gulbarga University, Gulbarga, 585106, (INDIA)

Email of Corresponding author :- E-mail: vrkulli@gmail.com

KEYWORDS:

dominating set, secure dominating set, inverse secure dominating set, inverse secure domination number.. Mathematics Subject Classification: 05C69, 05C78

Issue Date:

November, 2016

Pages:

294-298

ISSN:

2319-8044 (Online) – 2231-346X (Print)

Source:

Vol.28 – No.6

PDF

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DOI:

http://dx.doi.org/10.22147/jusps-A/280601

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.

Copy the following to cite this Article:

V.R. KULLI, “Equalityof Secure Domination and Inverse Secure Domination Numbers”, Journal of Ultra Scientist of Physical Sciences, Volume 28, Issue 6, Page Number 294-298, 2016


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V.R. KULLI, “Equalityof Secure Domination and Inverse Secure Domination Numbers”, Journal of Ultra Scientist of Physical Sciences, Volume 28, Issue 6, Page Number 294-298, 2016

Available from: http://www.ultrascientist.org/paper/605/equalityof-secure-domination-and-inverse-secure-domination-numbers


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.