Super Fair Dominating Set in Graphs

Article Sidebar

PDF
Published: Feb 19, 2019

Main Article Content

Enrico Limbo Enriquez
University of San Carlos

Abstract

In this paper, we initiate the study of super fair dominating set of a graph  by giving the super fair domination number of some special graphs. Further, we shows that given positive integers k,m, and n such that n\geq 2 and 1\leq k\leq m\leq n-1 there exists a connected graph G with |V(G)|=k, \gamma_{fd}(G)=k, and \gamma_{sfd}=m. Finally, we characterize the super fair dominating set of the join of two graphs.

Downloads

Download data is not yet available.

Article Details

How to Cite
Enriquez, E. L. (2019). Super Fair Dominating Set in Graphs. Journal of Global Research in Mathematical Archives(JGRMA), 6(2), 08–14. Retrieved from https://jgrma.com/index.php/jgrma/article/view/523
Issue
Vol. 6 No. 2 (2019): February-2019
Section
Research Paper
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Download Copyright
Author Biography

Enrico Limbo Enriquez, University of San Carlos

Associate Professor

Mathematics Department

University of San Carlos

Philippines

References

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

L. L. Kelleher and M.B. Cozzens, Dominating sets in social network graphs, Math. Social Sci., Vol. 16, no. 3 1988,

-279.

E. L. Enriquez, and S.R. Canoy, Jr., Secure Convex Domination in a Graph. International Journal of Mathematical

Analysis, Vol. 9 ( 2015), no. 7, 317-325.

E. L. Enriquez, and S. R. Canoy, Jr. , On a Variant of Convex Domination in a Graph. International Journal of

Mathematical Analysis, Vol. 9, 2015, no. 32, 1585-1592.

E. L. Enriquez, and S. R. Canoy, Jr. , Restrained Convex Dominating Sets in the Corona and the Products of

Graphs. Applied Mathematical Sciences, Vol. 9, 2015, no. 78, 3867 - 3873.

E.M. Kiunisala, and E. L. Enriquez, Clique Secure Domination in Graphs. Global Journal of Pure and Applied

Mathematics. Vol. 12, No. 3 (2016), pp. 2075–2084.

C. M. Loquias, and E. L. Enriquez, On Secure and Restrained Convex Domination in Graphs, International

Journal of Applied Engineering Research, Vol. 11, no. 7 (2016), 4707-4010.

R. T. Aunzo Jr. , and E. L. Enriquez, Convex Doubly Connected Domination in Graphs. Applied Mathematical

Sciences, Vol. 9, (2015), no. 135, 6723-6734.

E. M. Kiunisala and E. L. Enriquez, Inverse Secure Restrained Domination in the Join and Corona of Graphs,

International Journal of Applied Engineering Research 9(2016), pp.6676-6679

D. P. Salve and E. L. Enriquez, Inverse Perfect Domination in Graphs, Global Journal of Pure and Applied

Mathematics. Vol. 12, No. 1 (2016), pp. 1-10.

T. J. Punzalan and E. L. Enriquez, Inverse Restrained domination in graphs, Global Journal of Pure and Applied

Mathematics 3(2016) 2001-2009.

O. Ore. Theory of Graphs. American Mathematical Society, Provedence, R.I., 1962.

Y. Caro, A. Hansberg, and M.A. Henning, Fair Domination in Graphs. University of Haifa, 1-7, 2011.

M. Lemanska, V. Swaminathan, Y.B. Venkatakrishnan, R. Zuazua, Super Dominating sets in graphs. Proceedings of the

National Academy of Sciences, Vol. 85, 2015, no. 3, 353-357.

M. P. Baldado, Jr. and E. L. Enriquez, Super Secure Domination in Graphs, International Journal of Mathematical

Archive-8(12), 2017, pp. 145-149

E. L. Enriquez, Super Restrained Domination in the Corona of Graphs, International Journal of Latest Engineering

Research and Applications, Volume – 03, Issue – 05, May 2018, PP – 01-06

G. Chartrand and P. Zhang, A First Course in Graph Theory. Dover Publication, Inc., New York, 2012.

Most read articles by the same author(s)

1 2 > >>