Geodetic Connected Domination Number of a graph

Abstract

A pair x, y of vertices in a nontrivial connected graph is said to geodominate a vertex v of G if either v  {x,y} or v lies an x - y geodesic of G. A set S of vertices of G is a geodetic set if every vertex of G is geodominated by some pair of vertices of S. A subset S of vertices in a graph G is called a geodetic connected dominating set if S is both a geodetic set and a connected dominating set. We study geodetic connected domination on graphs.