z-DOMINATION IN GRAPHS

Article Sidebar

PDF
Published: Nov 18, 2018

Main Article Content

Nanet Altubar Goles
Cebu Technological University – Moalboal Campus
Enrico Limbo Enriquez
University of San Carlos
Carmelita Magdalunes Loquias
University of San Carlos
Grace Morta Estrada
University of San Carlos
Romeo C. Alota
University of San Carlos

Abstract

Let be a connected simple graph. A subset of a vertex setis a dominating set of if for every vertex there exists a vertexsuch thatis an edge of Let  be a minimum dominating set in The dominating set is called an inverse dominating set with respect to A disjoint dominating set of  is the setA -dominating set ofis a disjoint set such that The -domination number denoted by z is the minimum cardinality of -dominating set of -dominating set of  with cardinality equal to  z is called a z-of In this paper,  we show that every even integer and integer with  is realizable as -domination number and order ofrespectively. Further, we characterize the-dominating sets in the join and corona of two graphs and give some important results.

Downloads

Download data is not yet available.

Article Details

How to Cite
Goles, N. A., Enriquez, E. L., Loquias, C. M., Estrada, G. M., & Alota, R. C. (2018). z-DOMINATION IN GRAPHS. Journal of Global Research in Mathematical Archives(JGRMA), 5(11), 07–12. Retrieved from https://jgrma.com/index.php/jgrma/article/view/507
Issue
Vol. 5 No. 11 (2018): November-2018
Section
Research Paper
Download Copyright
Author Biographies

Nanet Altubar Goles, Cebu Technological University – Moalboal Campus

Faculty

College of Education, Arts and Sciences

Cebu Technological University - Moalboal Campus

Poblacion West, Moalboal, 6032, Cebu, Philippines

Enrico Limbo Enriquez, University of San Carlos

Associate Professor

Mathematics Department

University of San Carlos

Philippines

Carmelita Magdalunes Loquias, University of San Carlos

Assistant Professor

Mathematics Department

University of San Carlos

Philippines

Grace Morta Estrada, University of San Carlos

Assistant Professor

Mathematics Department

University of San Carlos

Philippines

Romeo C. Alota, University of San Carlos

Assistant Professor

Mathematics Department

University of San Carlos

Philippines

References

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

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, 9 (32), 1585-1592. http://dx.doi.org/10.12988/ajma.2015.54127

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.

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

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

E.L. Enriquez, Secure Restrained Convex Domination in Graphs. International Journal of Mathematical Archive, Vol.

, 2017, no. 7, 1-5.

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

Journal of Applied Engineering Research, Vol. 11, 2016, no. 7, 4707-4710

V.R. Kulli and S.C. Sigarkanti, Inverse domination in graphs, Nat. Acad. Sci. Letters 14(1991) 473-475.

T. Tamizh Chelvan, T. Asir and G.S. Grace Prema, Inverse domination in graphs, Lambert Academic Publishing, 2013.

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. http://www.ripublication.com/gjpam.htm

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

Mathematics 3(2016) 2001-2009.

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

Global Journal of Pure and Applied Mathematics, Vol. 12, 2016, no. 2, 1537-1545.

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 E.M. Kiunisala, Inverse secure domination in graphs, Global Journal of Pure and Applied

Mathematics 1(2016), pp.147-155

M. Hedetnieme, S.T. Hedetniemi, R.C. Laskar, L.R. Markus, P.J. Slater, Disjoint Dominating Sets in Graphs, Proc. of

ICDM, (2006), 87-100

J. Dayap and E.L. Enriquez, Disjoint Secure Domination in the Join of Graphs. Recoletos Multidisciplinary Research

Journal 2(2016)

R.C. Alota, and E.L. Enriquez, On Disjoint Restrained Domination in Graphs, Global Journal of Pure and Applied

Mathematics 3(2016), pp. 2385-2394.

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

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 > >>