gc - domination and GC-domination numbers of a graph

A.Muthukamatchi

doi:https://doi.org/10.14445/22315373/IJMTT-V51P522

International Journal of Mathematics Trends and Technology

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Volume 51 | Number 3 | Year 2017 | Article Id. IJMTT-V51P522 | DOI : https://doi.org/10.14445/22315373/IJMTT-V51P522

gc - domination and GC-domination numbers of a graph

A.Muthukamatchi

Abstract

Throughout this paper, we assume that G = (V,E) is a finite, simple connected graph with at least two vertices. Acharya and Sampathkumar [2] introduced the concept of graphoidal covers and graphoidal covering number of a graph. Arumugam and Suresh Suseela [4] introduced the concept of acyclic graphoidal cover and acyclic graphoidal covering number of a graph. An elaborate review of results in graphoidal covers with several interesting applications and a collection of unsolved problems is given in [3].

Keywords

An elaborate review of results in graphoidal covers with several interesting applications and a collection of unsolved problems is given in.

References

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[2] B. D. Acharya and E. Sampathkumar, Graphoidal covers and graphoidal covering number of a graph, Indian J. pure appl. Math., 18(10)(1987), 882 - 890.
[3] S. Arumugam, B. D. Acharya and E. Sampathkumar,Graphoidal covers of a graph - A creative review, Proceedings of the National workshop on Graph Theory and its Applications, Manonmaniam Sundaranar University, Tirunelveli, Eds. S. Arumugam, B. D. Acharya and E. Sampathkumar, Tata McGraw Hill, (1996), 1 - 28.
[4] S. Arumugam and J. Suresh Suseela, Acyclic graphoidal covers and path partitions in a graph, Discrete Math.,190(1998), 67 - 77.
[5] C. Berge, The Theory of graphs and its applications, Methuren, London (1962).
[6] B. Bollobas and E.J. Cockayne, Graph theoretic parameters concerning domination, independence and irredundance, J. Graph Theory, 3(1979), 241 - 250.
[7] G. Chartrand and L. Lesniak, Graphs and Digraphs, Fourth Edition, CRC Press, Boca Raton, 2004.
[8] E.J. Cockayne and S.T. Hedetniemi, Towards a theory of domination in graphs, Networks, 7(1977), 241 – 261. [9] F. Harary, Graph Theory, Addision - Wesley, Reading Mass,1972.
[10] T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, Inc., New York, (1997).
[11] T. W. Haynes, S. T. Hedetniemi and P. J. Slater. Domination in Graphs - Advanced Topics, Marcel Dekker, Inc.,New York, (1997).

Citation :

A.Muthukamatchi, "gc - domination and GC-domination numbers of a graph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 51, no. 3, pp. 172-176, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V51P522