IJPAM: Volume 106, No. 2 (2016)
Department of Mathematics
Bukidnon State University
Malaybalay City, PHILIPPINES
Department of Mathematics and Statistics
Mindanao State University-Iligan Institute of Technology
Andres Bonifacio Avenue, Tibanga, Iligan City 9200, PHILIPPINES
Abstract. A clique (convex) dominating set of is a -movable clique dominating set (resp. -movable convex dominating set) of if for every , either is a clique (resp. convex) dominating set or there exists a vertex such that is a clique (resp. convex) dominating set of . The minimum cardinality of a -movable clique (resp. -movable convex) dominating set of , denoted by (resp. ), is called the -movable clique domination number (resp. -movable convex domination number) of . A -movable clique dominating set in with cardinality is called a -set of .
This paper aims to characterize the -movable clique dominating sets of some graphs including those resulting from the join and composition of two graphs. The corresponding -movable clique domination number of the resulting graph is then determined. Further, it is shown that the concepts of -movable clique domination
and -movable convex domination are equivalent.
Received: September 2, 2015
AMS Subject Classification: 05C69
Key Words and Phrases: clique domination, convex domination, -movable clique domination, -movable convex domination
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DOI: 10.12732/ijpam.v106i2.10 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 463 - 471
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