OUTER-CONVEX DOMINATION IN THE CORONA OF GRAPHS

OUTER-CONVEX DOMINATION IN THE CORONA OF GRAPHS

J. Dayap

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Abstract

Let G be a connected simple graph. A subset S of a vertex set V (G) is called an outer-convex dominating set of G if for every vertex v 2 V (G)nS, there exists a vertex x 2 S such that xv is an edge of G and V (G)nS is a convex set. The outer-convex domination number of G, denoted by e con(G), is the minimum cardinality of an outer- convex dominating set of G. In this paper, we show that every integers a; b; c, and n with a   b   c   n ???? 1 is realizable as domination number, outer-connected domination number, outer-convex domination number, and order of G respectively. Further, we give the characterization of the outer-convex dominating set in the corona of two graphs and give its corresponding outer-convex domination number.

Keywords

Domination, outer-connected domination, outer-convex domination.