Proyecciones Journal of Mathematics Vol. 35, N^o 1, pp. 33-44, March 2016. Universidad Católica del Norte Antofagasta - Chile

Equi independent equitable dominating sets in graphs

S. K. Vaidya

Saurashtra University

N J Kothari 

L. E. College

India 

---

ABSTRACT

We introduce the concept of an equi independent equitable dominating set and define equi independent equitable domination number. We also investigate the graph families whose equi independent equitable domination number and equitable domination number are same.

Keywords : Equi independent equitable domination number, equitable domination number, domination number.

AMS subject classification number : 05C69; 05C38.

---

REFERENCES

[1]    C. Berge, Theory of Graphs and its Applications, Methuen, London, (1962).

[2]    E. J. Cockayne and S.T. Hedetniemi, Independence graphs, Congr. Numer., X, pp. 471-491, (1974).

[3]    E.J. Cockayne and S.T. Hedetniemi, Towards a theory of domination in graphs, Networks, 7, pp. 247-261, (1977).

[4]    W. Goddard and M. A. Henning, Independent domination in graphs: A survey and recent results, Discrete Mathematics, 313, pp. 839-854, (2013).

[5]    T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Fundamentals of domination in graphs, Marcel Dekker, New York, (1998).

[6]    O. Ore, Theory of graphs, Amer. Math. Soc. Transl. 38, pp. 206-212, (1962).

[7]    V.Swaminathan and K. Dharmalingam, Degree equitable domination on graphs, Kragujevac Journal of Mathematics, 35(1), pp. 191-197, (2011).

[8]    S. K. Vaidya and N. J. Kothari, Some Results on Equi Independent Equitable Dominating Sets in Graphs, Journal of Scientific Research, 7(3), pp. 77-85, (2015).

[9] S. K. Vaidya and N. J. Kothari, On equi independent equitable domi-nating sets in graphs, International Journal of Mathematics and Soft Computing, 6 (1), pp. 133-142, (2016).

[10]    S. K. Vaidya and N. J. Kothari, Equi independent equitable domination number of cycle and bistar related graphs, IOSR Journal of Mathematics, 11 (6), pp. 26-32, (2015).

[11]    D. B.West, Introduction to graph theory, 2nd ed., Prentice-Hall, New Delhi, India, (2003).

S. K. Vaidya

Department of Mathematics

Saurashtra University

Rajkot - 360005

Gujarat

India

e-mail : samirkvaidya@yahoo.co.in

N. J. Kothari

L. E. College Sama Kathe

Morbi-363642

Gujarat

India

e-mail : nirang_kothari@yahoo.com

Received : March 2015. Accepted : December 2015