TRIPLE CONNECTED DOMINATION NUMBER OF A GRAPH
Creators
- 1. Research Scholar, Department of Mathematics, PRIST University, Thanjavur, Tamilnadu
- 2. Assistant Professor, Department of Mathematics, PRIST University, Thanjavur, Tamilnadu
Description
The concept of triple connected graphs with live application was introduced in by considering the available of roots containing any three vertices of a graph G. In this thesis, we introduce a new dominating parameter, called Smarandachely triple connected domination number of a graph. A subset S of V of a nontrivial G-graph is said to be Smarandachely triple connected dominated set, if S is a dominating set and the induced sub graph S is triple connected. The nominal cardinality take over all Smarandachely triple connected dominant sets is called the Smarandachely triple connected domination number and is denoted by γtc. We assumed this number for some standard graphs and obtain sustained bounds for general graphs. It’s have the relationship with other graph theoretical parameters also investigated.
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Additional details
References
- 1. Mahadevan G, Selvam A, Paulraj Joseph J, Ayisha B and Subramanian T, Complementary triple connected domination number of a graph, accepted for publication in Advances and Applications inDiscrete Mathematics, ISSN0974-1658(2012). 2. Mahadevan. G, Selvam Avadayappan, Nagarajan. A, Rajeswari. A, Subramanian. T, Paired Triple connected domination number of agraph, International Journal of Computational Engineering Research, Vol.2, Issue 5, Sep. 2012, pp.1333-1338(2012). 3. Mahadevan G., Selvam Avadayappan, Hajmeeral. M., andSubramanian T, Dom strong triple connected domination number of a graph, American Journal of Mathematics and Mathematical Sciences, ISSN 2278-0874, Vol. 1, Issue No. 2, July – Dec. 2012,pp.29-37. 4. Mahadevan G., Selvam A., Bhagavathi Ammal V. G, and Subramanian T, weak triple connected domination number of a graph, International Journal of Modern Engineering Research (IJMER) Vol.3, Issue 1, Jan-Feb.2013 pp-342-345 ISSN: 2249-6645. 5. Mahadevan G., Selvam A., Bhagavathi Ammal V. G, and SubramanianT, Strong triple connected domination number of a graph, International Journal of Computational Engineering Research (ijceronline.com) Vol.3 Issue. 1(2012). 6. Nordhaus E. A. and Gaddum J. W. On complementary graphs, Amer. Math. Monthly, 63: 175–177(1956). 7. Paulraj Joseph J., Angel Jebitha M.K., Chithra Devi P. and Sudhana G. Triple connected graphs, Indian Journal of Mathematics and Mathematical Sciences, ISSN 0973-3329, Vol. 8, No.1, pp 61-75(2012). 8. Sampathkumar, E.; Walikar, HB The connected domination number of a graph, J. Math. Phys. Sci 13 (6): 607–613(1979). 9. Teresa W. Haynes, Stephen T. Hedetniemi and Peter J. Slater, Fundamentals of dominationin graphs, Marcel Dekker, New York (1998).