The paper concentrates on the theory of domination in graphs. In this paper we define a new parameter on domination called matching domination set, matching domination number and we have investigated some properties on matching domination of cartesian product of two graphs. The following are the results: If ui1 and uj2 then degG1(C)G2 (ui, vj ) = degG1 (ui).degG2 (vj ) If G1, G2 are simple finite graphs without isolated vertices. G1(C)G2 is a simple finite graph without isolated vertices.The cartisean product graph of two simple graphs is not a complete graph. If G1 and G2 are bipartite graphs them G1(C)G2 is a bipartite graph. If G1 and G2 are any two graphs without isolated vertices then γm[G1(C)G2] ≤ | V1 | .γmd(G2); γmd(G1). | V2 |
Keywords : Cartesian product of graphs,omination Set,Domination number, Complete graphs, Isolated vertices, degree, regular graphs, bipartite graphs.