EDGE DOMINATION IN SOME BRICK PRODUCT GRAPHS

Özet

LetG= (V,E) be a simple connected and undirected graph. A setFofedges inGis called an edge dominating set if every edgeeinE−Fis adjacent to atleast one edge inF. The edge domination numberγ′(G) ofGis the minimum cardinalityof an edge dominating set of G. The shadow graph ofG, denotedD2(G) is the graphconstructed fromGby taking two copies ofG, sayGitself andG′and joining eachvertexuinGto the neighbors of the corresponding vertexu′inG′. LetDbe the set ofall distinct pairs of vertices inGand letDs(called the distance set) be a subset ofD.The distance graph ofG, denoted byD(G,Ds) is the graph having the same vertex setas that ofGand two verticesuandvare adjacent inD(G,Ds) wheneverd(u,v)∈Ds.In this paper, we determine the edge domination number of the shadow distance graphof the brick product graphC(2n,m,r).