z-DOMINATION IN GRAPHS

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Published: Nov 18, 2018

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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.

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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

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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

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