Complementary connected domination and connectivity domination number of an arithmetic graph G=Vn

Abstract

A subset S of V is said to be a complementary connected dominating set if every vertex not in S is adjacent to some vertex in S and the sub graph induced by V − S is connected. The complementary connected domination number of the graph is denoted by γccd(G) and is defined as the minimum number of vertices which form a ccd-set. A set S of vertices in a graph G is a connectivity dominating set if every vertex not in S is adjacent to some vertex in S and the sub graph induced by V −S is not connected. The connectivity domination number κγ(G) is the minimum size of such set.