Secure Support Strong Domination in Graphs

Authors

  • R. Guruviswanathan Department of Mathematics, Jeppiaar Maamallan Engineering College, Sriperumbudur, Tamilnadu, India; Sri Chandrasekharendra Saraswathi Viswa Mahavidyalaya, Kanchipuram, India
  • M. Ayyampillai Department of Mathematics, Arunai Engineering College, Thiruvannamalai, Tamilnadu
  • V. Swaminathan Ramanujan Research Centre in Mathematics, Saraswathi Narayanan College, Madurai, Tamilnadu

DOI:

https://doi.org/10.26713/jims.v9i3.759

Keywords:

Support, Strong Dominating set, Secure support strong dominating set, Dominator coloring, Color class domination

Abstract

Let \(G=(V, E)\) be a simple finite undirected graph. Let \(D\) be a subset of \(V(G)\). \(D\) is called a secure support strong dominating set of \(G\) (also called very excellent support strong dominating set), if \(D\) is a support strong dominating set of \(G\) and for any \(u\) in \(V-D\), there exists a, \(v \in D\) such that \(uv \in E(G)\) and \(supp(u) \geq supp(v)\) and \((D-\{v\})\cup \{u\}\) is support dominating set. The minimum cardinality of a secure support strong dominating set of \(G\) is called the secure support strong domination number of \(G\) and is denoted by \(\gamma_{sec}^{ss}(G)\). In this paper, properties of the new parameters are derived and its relationships with other parameters are studied.

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References

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CITATION

How to Cite

Guruviswanathan, R., Ayyampillai, M., & Swaminathan, V. (2017). Secure Support Strong Domination in Graphs. Journal of Informatics and Mathematical Sciences, 9(3), 539–546. https://doi.org/10.26713/jims.v9i3.759

Issue

Vol. 9 No. 3 (2017)

Section

Research Articles

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