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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 5 | Year 2019 | Article Id. IJMTT-V65I5P521 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I5P521

Open Support of a Graph under Multiplication


S. Balamurugan , M. Anitha , C. Karnan , P. Palanikumar
Abstract

In this paper, the open support of a vertex 𝑣 under multiplication and open support of a graph 𝐺 under multiplication is defined and studied. Also, we find the value of open support of some namely graphs like Dutch windmill graph, Butterfly graph and Ladder graph. Moreover, we generalized the value of open support under multiplication for any given graph 𝐺. AMS Subject Code: 05C07

Keywords
Vertex Degree, Open Support under multiplication of a Vertex, Open Support under multiplication of a Graph.
References

[1] M. Anitha, S. Balamurugan: Strong (Weak) Efficient Open Domination on Product Graphs, International Journal of Pure and Applied Mathematics, (J.No. 23425), IISN 1311 - 8080, communicated.
[2] S. Balamurugan, M. Anitha, C. Karnan and P. Aristotle A Note on Open Support of a Graph under Addition I, Communicated
[3] S. Balamurugan, M. Anitha, C. Karnan and P. Aristotle: A Note on Open Support of a Graph under Addition II, Communicated
[4] S. Balamurugan, M. Anitha, C. Karnan and P. Palanikumar: Closed Support of a Graph Under Addition I , Communicated
[5] S. Balamurugan, M. Anitha, C. Karnan and P. Palanikumar: Closed Support of a Graph Under Addition II , Communicated
[6] R. Balakrishnan, K. Ranganathan, A Textbook of Graph Theory, Springer,2011.
[7] S. Balamurugan, A study on chromatic strong domination in graphs, Ph.D Thesis, Madurai Kamaraj University, India 2008.
[8] J.A. Bondy, U.S.R. Murthy, Graph theory with Applications, North-Holland, 1982.
[9] F. Harary : Graph Theory, Addsion Wesley, Reading, Mass, (1972).
[10] T. W. Haynes, S. T. Hedetniemi, P. J. Slater: Fundamentals of Domination in Graphs, Marcel Dekker, New York, (1998).
[11] C. Y. Ponnappan: Studies in Graph Theory Support Strong Domination in Graphs, Ph.D thesis, Madurai Kamaraj University (2008).

Citation :

S. Balamurugan , M. Anitha , C. Karnan , P. Palanikumar, "Open Support of a Graph under Multiplication," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 5, pp. 134-138, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I5P521

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