DETOUR ECCENTRIC DOMINATION IN GRAPHS

Authors

  • A Mohamed Ismayil P.G. and Research Department of Mathematics, Jamal Mohammed College, Tiruchirappalli, Tamil Nadu 620020, India.
  • R Priyadharshini Department of Mathematics, Dhanalakshmi Srinivasan Engineering College, Perambalur, Tamil Nadu 621107, India.

DOI:

https://doi.org/10.48165/

Keywords:

Dominating set, Domination number, Detour eccentric set, Detour eccentric dominating set, Detour eccentric domination number

Abstract

In this paper, the detour eccentric point set and detour eccentric dominating sets are defined. The detour  eccentric domination numbers are also defined. The detour eccentric domination numbers for some standard  graphs are determined. Also some theorems related to detour eccentric domination number are stated and proved.  

References

. Alikhani, S., Peng, Y.H. and Atan, K.A.N. (2008). On the domination number of some graphs, International Mathematical Forum, 3(38), 1879-1884.

. Frendrupa, Allan, Henningb, Michael A., Randerathc, Bert and Vestergaarda, Preben Dahl (2009). An upper bound on the domination number of a graph with minimum degree 2 , Discrete Mathematics, 309, 639–646.

. Bhanumathi, M. and Muthammai, S. (2011). On eccentric domination in trees, International Journal of Engineering Science, Advanced Computing and Bio Technology, 2(1), 38-46. [4]. Bondy, J.A. and Murthy, U.S.R. (1976). Graph theory with Applications, The Macmillan Press Ltd. Great Britain.

. Buckly, F. and Harary, F. (1990). Distance in graphs, Addition-Wesley Publishing Company, Redwood City, San Francisco Peninsula.

. Harary, F. (1972). Graph Theory, Addition-Wesley Publishing Company Reading Mass. [7]. Haynes, T.W., Hedetniemi, S.T. and Slater, P.J. (1998) Fundamentals of Domination in Graphs. Marcel Dekker, Inc., New York.

. Janakiraman, T.N., Bhanumathi, M. and Muthammai, S. (2010). Eccentric domination in graphs, International Journal of Engineering Science, Advanced Computing and Bio Technology, 1(2), 55-70.

. Johnand, J. and Arianayagam, N. (2017). The detour domination number of a graph, Discrete Mathematics, Algorithms and Applications, Vol. 9, No. 1 (2017), Article ID 1750006 (7 pages). [10]. NellaiMurugan, A., Esakkimuthu, A. and Mahadevan, G. (2016). Detour domination number of a Graph ,Internation Journal of Science, Engineering and Technology Research(IJSETR), 5(2), 439-442. [11] Ore, O. (1962). Theory of Graphs. Amer. Math. Soc. Colloq. Publ., 38, Amer. Math. Soc., Providence, RI.

Published

2019-07-14

How to Cite

Ismayil, A.M., & Priyadharshini, R. (2019). DETOUR ECCENTRIC DOMINATION IN GRAPHS . Bulletin of Pure & Applied Sciences- Mathematics and Statistics, 38(1), 342–347. https://doi.org/10.48165/