AUTHOR AND AFFILIATION |
V.R. KULLI 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 |
Click Here Download PDF |
|
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
Copy the following to cite this URL:
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.