Outer-convex domination in graphs
Jonecis Dayap, Enrico L. Enriquez · Discrete Mathematics Algorithms and Applications · 2019
Let [Formula: see text] be a connected simple graph. A set [Formula: see text] of vertices of a graph [Formula: see text] is an outer-convex dominating set if every vertex not in [Formula: see text] is adjacent to some vertex in [Formula: see text] and [Formula: see text] is a convex set. The outer-convex domination number of [Formula: see text], denoted by [Formula: see text], is the minimum cardinality of an outer-convex dominating set of [Formula: see text]. An outer-convex dominating set of cardinality [Formula: see text] will be called a [Formula: see text]-[Formula: see text]. In this paper, we initiate the study and characterize the outer-convex dominating sets in the join of the two graphs.