Matching Domination of Lexicograph Product of Two Graphs

Abstract

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 Lexicograph product of two graphs. The following are the results: ? NG(ui, vj ) = {NG1 (ui)XV2} ? {(ui)XNG2 (vj )} ? degG(ui, vj ) =| NG1 (u1) || V2 | ? | NG2 (vj ) ? degG(ui, vj ) = 0 if and only if degG1 (ui) = 0 and degG2 (vj ) = 0 ? If G1, G2 are simple finite graphs without isolated vertices then G1(L)G2 is a finite graph without isolated vertices. ? If G1, G2 are any two graphs without isolated vertices then ?m | G1(L)G2 |= ?m(G1)