• SECURE RESTRAINED CONVEX DOMINATION IN GRAPHS

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.