Inverse Clique Domination in Graphs
DOI:
https://doi.org/10.32871/rmrj1604.02.03Keywords:
dominating set, clique dominating set, inverse clique dominating setAbstract
Let G be a connected simple graph. A nonempty subset S of the vertex set V (G) is a clique in G if the graph <S> induced by S is complete. A clique S in G is a clique dominating set if it is a dominating set. Let C be a minimum clique dominating set in G. The clique dominating set   S⊆V(G)\C is called an inverse clique dominating set with respect to C. The minimum cardinality of inverse clique dominating set is called an inverse clique domination number of G and is denoted by γcl −1 (G). An inverse clique dominating set of cardinality γcl −1(G) is called γcl −1-set of G. In this paper we investigate the concept and give some important results.
References
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[2] E.J. Cockayne, and S.T. Hedetniemi, Towards a theory of domination in graphs, Networks 7, (1977) 247-261.
[3] E.S. Wolk, A note on the comparability graph of a tree, Proc. Amer. Math. Sot. 16 (1965) 17-20.
[4] L.L. Kelleher and M.B. Cozzens, Dominating sets in social network graphs, Math. Social Sci., Vol. 16, no. 3 1988, 267-279.
[5] M.B. Cozzens and L. Kelleher, Dominating cliques in graphs, Discrete Mathematics, 86 (1990), 101 - 116. http://dx.doi.org/10.
[6] O. Ore. Theory of Graphs. American Mathematical Society, Provedence, R.I., 1962.13
[7] T. V. Daniel and Sergio R. Canoy, Jr., Clique domination in a Graph, Applied Mathematical Sciences, Vol. 9, 2015, no. 116, 5749 - 5755
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Published
2016-12-31
How to Cite
Loquias, C., Enriquez, E., & Dayap, J. (2016). Inverse Clique Domination in Graphs. Recoletos Multidisciplinary Research Journal, 4(2). https://doi.org/10.32871/rmrj1604.02.03
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