SUPER CONNECTED DOMINATION IN GRAPHS

Main Article Content

Enrico Limbo Enriquez
Bea Elaine Parrilla Fedellaga
Carmelita M. Loquias
Grace M. Estrada
Margie L. Baterna

Abstract

In this paper, we initiate the study of super connected dominating set of a graph  by giving the super connected domination number of some special graphs. Further, we shows that given positive integers  and  such that  and  there exists a connected graph  with ,  and .  Finally, we characterize the super connected dominating set of the join, corona, and Cartesian product of two graphs.

Downloads

Download data is not yet available.

Article Details

How to Cite
Enriquez, E. L., Fedellaga, B. E. P., Loquias, C. M., Estrada, G. M., & Baterna, M. L. (2019). SUPER CONNECTED DOMINATION IN GRAPHS. Journal of Global Research in Mathematical Archives(JGRMA), 6(8), 01–07. Retrieved from https://jgrma.com/index.php/jgrma/article/view/536
Section
Research Paper
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, Domination in graphs and its application to social network theory, Ph.D. Thesis, Northeastern University 1985.

L.L. Kelleher and M.B. Cozzens, Dominating sets in social network graphs, Math. Social Sci., Vol. 16, no. 3 1988, 267-279.

R. Laskar, and S.T. Hedetniemi, Connected domination in graphs, Tech. Report 414, Clemson Univ., Dept. Mathematical Sci., 1983.

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.

C. M. Loquias, E. L. Enriquez, and J. Dayap. Inverse Clique Domination in Graphs. Recoletos Multidisciplinary Research Journal. Vol. 4, No. 2 (2017), pp 23-34.

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.

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

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

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

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, 3(5), 2018, pp. 1 – 6.

E.L. Enriquez, Super Fair Dominating Set in Graphs, Journal of Global Research in Mathematical Archives, 6(2), 2019, pp 8 – 14.

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