Abstract:

Let G = V;E be a simple connected and undirected graph. A set F of edges in G is called an edge dominating set if every edge e in E - F is adjacent to at least one edge in F. The edge domination number 0 G of G is the minimum cardinality of an edge dominating set of G. The shadow graph of G, denoted D2 G is the graph constructed from G by taking two copies of G, say G itself and G' and joining each vertex u' in G' to the neighbors of the corresponding vertex u 0 in G'. Let D be the set of all distinct pairs of vertices in G and let Ds called the distance set be a subset of D. The distance graph of G, denoted by D G;Ds is the graph having the same vertex set as that of G and two vertices u and v are adjacent in D G;Ds whenever d u; v 2 Ds. In this paper, we determine the edge domination number of the shadow distance graph of the brick product graph C 2n; m; r .

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