A set D V of a graph G = (V, E) is called a dominating set of G if every vertex in V D is adjacent to at least one vertex in D. A dominating set D of a graph G is convex dominating set if all vertices from u-v geodesic belong to D for every two vertices u, v D. A convex dominating set D of a graph G is nonsplit convex dominating set if the induced subgraph GV D is connected. The nonsplit convex domination number of G is the minimum cardinality of a nonsplit convex dominating set D and it is denoted by ₍ₒ₂₎₍ (G). In this paper, we initiate the study on this parameter. We establish bounds for nonsplit convex domination number, ₍ₒ₂₎₍ (G), of standard graph structures. Further, we also present conditions for identifying or constructing a nonsplit convex dominating set in any connected graph G.
Dahal et al. (Sat,) studied this question.