• SECURE RESTRAINED CONVEX DOMINATION IN GRAPHS

ENRICO L. ENRIQUEZ*

Abstract


Let  be a connected simple graph. A restrained convex dominating set  in a connected graph  is a secure restrained convex dominating set, if for each element  in  there exists an element  in  such that   and  is a restrained convex dominating set.  The secure restrained convex domination number of , denoted by , is the minimum cardinality of a secure restrained convex dominating set in . A secure restrained convex dominating set of cardinality  will be called a -. In this paper, we give some realization problems will be given. In particular, we show that given positive integers  and  such that  and  there exists a connected graph  with  and. Further, we characterize the secure restrained convex dominating sets in the join of two graphs and give some important results.


Keywords


convex domination, restrained convex dominating set, secure restrained convex dominating set.

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