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.

Downloads

Download data is not yet available.

References

E. Sampathkumar and L. Pushpa Latha, Strong weak domination and domination balance in a graph, Discrete Mathematics 161 (1996), 235 – 242

R.M. Gera, On Dominator colorings in Graphs, Graph Theory Notes, New York, 52 (2007), 25 – 30.

P.J.P. Gobler and C.M. Mynhardt, Secure domination critical graphs, Discrete Mathematics 309 (2009), 5820 – 5827.

F. Harary, Graph Theory, Addison - Wesley, Reading Mass. (1972).

T.W. Haynes, S.T. Hedetneimi and P.J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker Inc., New York (1998).

T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics, Marcel Dekker Inc., New York (1998).

S.T. Hedetniemi and S.M. Hedetniemi, Dominating partitions of graphs, Technical Report (1979), unpublished manuscript.

H.B. Merouane and M. Chellali, On secure domination in graphs, Information Processing Letters 115 (2015), 786 – 790.

C.Y. Ponnappan, Studies in Graph Theory Support Strong Domination in Graphs, Ph.D thesis, Madurai Kamaraj University (2008).

V. Swaminathan, R. Sundareswaran, Color class domination in graphs, Mathematical and Experimental Physics, Narosa Publishing House (2010).

Downloads

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

Section

Research Articles