Outer-Clique Domination in Graphs

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Published: Jul 31, 2018

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Enrico Limbo Enriquez
University of San Carlos
Jovita N. Ravina
University of San Carlos
Valerie Verallo Fernandez
University of San Carlos

Abstract

Let  be a simple graph. A set of vertices of a graph is an outer-clique dominating set if every vertex not in  is adjacent to some vertex inand the subgraph induced by is clique. In this paper, we will show that given positive integers  andsuch thatthere exists a connected nontrivial graph  with and  Further, we give characterization the outer-clique dominating sets resulting from the join of two graphs and give some important results.  In this paper, we show that for each set of integers and  with the integers  and  are realizable as domination number, outer-clique domination number, and order of , respectively. Further, we give the characterization of the outer-clique dominating set with outer-clique domination numbers of 1 and 2. Finally, we characterize outer-clique dominating sets of the join of two graphs.

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How to Cite
Enriquez, E. L., Ravina, J. N., & Fernandez, V. V. (2018). Outer-Clique Domination in Graphs. Journal of Global Research in Mathematical Archives(JGRMA), 5(7), 102–107. Retrieved from https://www.jgrma.com/index.php/jgrma/article/view/493
Issue
Vol. 5 No. 7 (2018): July-2018
Section
Research Paper

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Author Biographies

Enrico Limbo Enriquez, University of San Carlos

Associate Professor

Mathematics Department

University of San Carlos

Philippines

Jovita N. Ravina, University of San Carlos

Mathematics Department

Assistant Professor

Valerie Verallo Fernandez, University of San Carlos

Mathematics Department

Full Professor

References

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

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

Sci., 1983.

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

J. Cyman, The Outer-connected Domination Number of a graph. Australas. J.Combin., 38(2007), 35-46.

F. Harary and J. Nieminen, Convexity in graphs. J. Differ Geom. 16(1981), 185-190.

M. Lemanska, Weakly convex and convex domination numbers. Opuscula Mathematica, 24 (2004), 181-188.

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.

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.

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

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

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

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

L.L. Kelleher, Domination in graphs and its application to social network theory, Ph.D. Thesis, Northeastern University,

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

E.S. Wolk, A note on the comparability graph of a tree, Proc. Amer. Math. Sot. 16 (1965) 17-20.

M.B. Cozzens and L. Kelleher, Dominating cliques in graphs, Discrete Mathematics, 86 (1990), 101 - 116.

T.V. Daniel, and S.R. Canoy,Jr., Clique Domination in a Graph. Applied Mathematical Sciences, Vol. 9, 2015, no. 116,

- 5755.

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.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.

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

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