Abstract

Let G = (V, E) be an undirected, simple and connnected graph. A set C ⊆ V of vertices in G is called a convex set if I(C) = C where I(C) is the set of all vertices in the u-v geodesic path of G for all u, v ∈ C. For any set C ⊆ V, the convex hull of C denoted by [C] is defined as the smallest convex subset of V(G) containing C. Let S be a minimum vertex covering transversal dominating set viz. a γvct-set. Then the convex hull of S is defined as the smallest convex set containing S. We define the convex hull number of G with respect to γvct-sets, denoted by CHγvct(G) as CH γvct(G) = min.{|C|: C = [S] is the convex hull of γvct-set S} where the minimum is taken over all the vct-sets of G. If [S] = S, then S is called a convex γvct-set. If [S] = V(G), then S is called a hull γvct-set. In this paper, the convex hull of γvct-sets and the convex hull number with respect to γvct-sets in various graphs are analysed.

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