ON RESTRAINED CLIQUE DOMINATION IN GRAPHS

Enrico Limbo Enriquez

Abstract


Abstract:  Let  be a connected simple graph. A nonempty subset  of the vertex set  is a clique in  if the graph  induced by  is complete. A clique  in  is a clique dominating set if it is a dominating set. A clique dominating set  of  is a restrained clique dominating set if for each , there exists  such that  The minimum cardinality of a restrained clique dominating set in , denoted by  is called the restrained clique domination number of . In this paper we investigate the concept and give some important results.


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References


REFERENCES

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

E.L. Enriquez. Secure restrained domination in the Join and Corona of graphs. Global Journal of Pure and Applied

Mathematics, 12 (1), 507-516

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.

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

G.S. Domke, J.H. Hattingh, S.T. Hedetniemi, R.C. Laskar, L.R. Markus, Restrained domination in graphs. Discrete Math.

(1999) 61-69.

Labendia, M.A., Canoy, S.R., Convex Domination in the Composition and Cartesian Product of Graphs, Czechoslovak

Mathematical Journal, 62(2012), 1003-1009.

J.A. Telle, A. Proskurowski, Algorithms for Vertex Partitioning Problems on Partial-k Trees, SIAM J. Discrete

Mathematics, 10(1997), 529-550.

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

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

S. R. Canoy, Jr., and I. J. L. Garces. Convex sets under some graph operations. Graphs and Combinatorics, 18 (2002),

-793.

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

- 5755.


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