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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 32 | Number 2 | Year 2016 | Article Id. IJMTT-V32P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V32P511

Line Join Connected Domination on a Graph


D. S. T. Ramesh, S. Athisayanathan, A. Anto Kinsley, J. Vinolin
Abstract

In this paper we introduce a new concept line join graph of a set of vertices S of a graph. We construct a new graph, called the line join graph of S and define a new domination parameter called line join connected domination number. We determine this number for some standard graphs and obtain bounds for general graphs. We prove various important results connecting with the domination number.

Keywords
Connected graph, complete, bipartite, wheel graphs, distance, dominating set
References

[1] Buckley.F, Harary.F, Distance in graphs, Addison-Wesley Publishing Company, (1990).
[2] Cockayne.E.J, Hedetniemi.S.T, Towards a theory of domination in graphs, Networks, 7:247-261.(1997).
[3] Ermelinda Delavina, Ryan Pepper and Bill Waller, Lower bounds for the domination number, Discussiones Mathematicae Graph Theory, January (2010).
[4] Gary Chartand, Ping Zhang, Introduction to Graph theory, McGraw Hill Education (India) Private Limited , New Delhi (2006).
[5] Harary.F, Graph theory, Addison-Wesley Publishing Company Reading, Mass (1972).
[6] Janakiraman T.N, Bhanumathi.M and Muthammai.S, Eccentric Domination in Graphs, International Journal of Engineering Science, Advanced Computing and Bio- Technology Vol. 1, No.2, April-June 2010, pp. 55-70.
[7] Teresa W.Haynes, Stephen T.Hedetniemi, Peter J. Slater, Fundamentals of Domination in graphs, Marcel Dekker, Inc. (1998).
[8] Teresa W.Haynes, Stephen T.Hedetniemi, Peter J. Slater, Domination in graphs Advanced Topics, Marcel Dekker, Inc. (1998).

Citation :

D. S. T. Ramesh, S. Athisayanathan, A. Anto Kinsley, J. Vinolin, "Line Join Connected Domination on a Graph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 32, no. 2, pp. 66-70, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V32P511

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