WEAKLY CONVEX DOUBLY CONNECTED DOMINATION IN THE JOIN AND CORONA OF GRAPHS

Enrico Limbo Enriquez, Grace M. Estrada, Carmelita M. Loquias

Abstract


Let be a connected simple graph. A weakly convex dominating set  of is a weakly convex doubly connected dominating set if  is a doubly connected dominating set of The weakly convex doubly connected domination number of  denoted by , is the smallest cardinality of a convex doubly connected dominating set  of . In this paper, we show that for each set of integers and  with the integers  and  are realizable as weakly convex doubly connected domination number, convex doubly connected domination number, and order of , respectively. Further, we give the characterization of the weakly convex doubly connected dominating set with weakly convex doubly connected domination numbers of 1 and 2. Finally, we characterize the weakly convex doubly connected dominating sets of the join and corona of two graphs.

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References


B. Arriola, and S. R. Canoy Jr., Doubly Connected Domination in the Corona and Lexicographic Product of Graphs.

Applied Mathematical Sciences, Vol. 8 (2014), no. 31, 1521-1533.

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

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.

F. Harary, and J. Nieminen, Convexity in graphs. J. Differ Geom. 16 (1982),185-190.

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

G. Chartrand, and P. Zhang, Convex sets in graphs. Congressus Numerantium, 136(1999), 19-32.

J. Cyman, M. Lemanska, and J. Raczek, On the Doubly Connected Domination Number of a Graph. Cent. Eur. J. Math,

(2006), 34-45.

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

R. Leonida, Weakly Convex Domination and Weakly Connected Independent Domination in Graphs, Ph.D. Thesis, MSU-

Iligan Institute of Technology (2013).

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

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

S.R. Canoy Jr., and I. Garces, Convex Sets Under Some Graphs Operations. Graphs Comb. 18, (2002), 787-793.


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