Co-Secure Set Domination in Graphs
D. Bhuvaneswari1, S. Meenakshi2
1D. Bhuvaneswari, Research Scholar, Department of Mathematics, Vels Institute of Science, Technology & Advanced Studies, Chennai (Tamil Nadu), India.
2S. Meenakshi, Associate Professor, Department of Mathematics, Vels Institute of Science, Technology & Advanced Studies, Chennai (Tamil Nadu), India.
Manuscript received on 18 January 2020 | Revised Manuscript received on 01 February 2020 | Manuscript Published on 05 February 2020 | PP: 66-68 | Volume-8 Issue-4S5 December 2019 | Retrieval Number: D10251284S519/2019©BEIESP | DOI: 10.35940/ijrte.D1025.1284S519
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Throughout this paper, consider G = (V,E) as a connected graph. A subset D of V(G) is a set dominating set of G if for every M V / D there exists a non-empty set N of D such that the induced sub graph <MUN> is connected. A subset D of the vertex set of a graph G is called a co-secure dominating set of a graph if D is a dominating set, and for each u’ D there exists a vertex v’V / D such that u’v’ is an edge and D u’v’ is a dominating set. A co-secure dominating set D is a co-secure set dominating set of G if D is also a set dominating set of G. The co-secure set domination number G s cs γ is the minimum cardinality of a co-secure set dominating set. In this paper we initiate the study of this new parameter & also determine the co-secure set domination number of some standard graphs and obtain its bounds.
Keywords: Co-secure Dominating Set, Dominating Set, Set Dominating Set.
Scope of the Article: Cryptography and Applied Mathematics