THE GLOBAL CONNECTED DOMINATION IN CARTESIAN GRAPHS

A subset S of vertices of a Cartesian graph G?H is called a global connected dominating set if S is both a global dominating set and a connected dominating set. The global connected domination number is the minimum cardinality of a global connected dominating set of G?H and is denoted by gamma sub( gc)(G?H). In this paper, sharp bounds for gamma sub( gc)(G?H) are supplied and all Cartesian graphs attaining these bounds are characterized. We also characterize the Cartesian product on complete graph G and H of order mn with gamma sub( gc) =n where 2 less than or equal to n less than or equal to m. m is the order of G and n is the order of H.