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Reseach Article
The Split Domination in Arithmetic Graphs
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 29 - Number 3 |
| Year of Publication: 2011 |
| Authors: Dr. K.V.Suryanarayana Rao, Prof. V. Sreenivansan |
10.5120/3542-4851
|
Dr. K.V.Suryanarayana Rao, Prof. V. Sreenivansan . The Split Domination in Arithmetic Graphs. International Journal of Computer Applications. 29, 3 ( September 2011), 46-49. DOI=10.5120/3542-4851
Abstract
The paper concentrates on the theory of domination in graphs. The split domination in graphs was introduced by Kulli and Janakirm[5].In this paper; we have investigated some properties of the split domination number of an Arithmetic Graph and obtained several interesting results. The split domination of these arithmetic graphs have been studied as it enables us to construct graphs with a given split domination number in a very simple way. We have obtained an upper bound for the split domination number of the Vm graph as r+1,where m is a positive integer and m =p_1^(a_1 ).p_2^(a_2 )……p_r^(a_r ) is the canonical representation, where p_1,p_2,…,p_r are distinct primes and a_i^' s>1.
References
- Apostol, T.M., Introduction to analytic number theory, Springer – verlag, Berlin, Heidelberg (1980).
- Bondy and Murty: Graph theory with applications, Macmillan (1976).
- Haynes, T.W., Hedetniemi, S.T. and Slater, P.J., Fundamentals of domination in graphs ; Marcel Dekkar, Inc-New York (1998).
- Harary, F., Graph Theory, Addison – Wesley, Massachusetts, (1969).
- Kulli, V.R. and Janakiram, B., The split domination number of a graph; Graph theory notes of New York, XXXII, 16-19 (1997); New York Acadamy of Sciences.
- Laskar, R.C. and Walikar, H.B., On domination related concepts in graph theory, in : Lecture notes in Match., 885 (1981), 308-320.
- Sampathkumar, E., On some new domination parameters of a graph – A Survey, Proceedings of a symposium on graph theory and combinatorics, Kochi, Kerala, India, 17-19 may 1991, pp. 7-13.
- Vasumathi, N., and Vangipuram, S., Existence of a graph with a given domination parameter, Proceedings of the Fourth Ramanujan Symposium on Algebra and its Applications; University of Madras, Madras, 187-195 (1995).
- Vijaya Saradhi and Vangipuram: ‘Irregular graphs’. Graph Theory Notes of New York, Vol. 41, 2001, pp. 33-36.
- Chatrand, G., and Lesniak, L., Graphs and digraphs, Chapman and Hall, Madras (1996).
- Cockayne, E.J., and Hedetniemi, S.T., Towards a theory of domination in graphs, Networks, Fall (1977), 247-271.
- Cockayne, E.J., Domination of undirected graphs, A survey, Lecture notes in Math., 642 (1978), 141-147.
- Cockayne, E.J., Dawes, R.W. and Hedetniemi, S.T., Total domination in graphs, Networks, 10, (1980), 211-219.
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