Abstract
Let {\ \ \gamma}^e(G) be the edge domination number of a graph. A “web graph” W(s,t) is obtained from the Cartesian product of cycle graph of order s\ and path graph of order\ t. In this paper, edge domination number of the web graph is determined. Mathematical subject classification: 05C69
Highlights
Number” of a graph GG which we denote by γγee(GG) is the minimum cardinality taken over all edge dominating sets of GG
If tt ≡ 1, the set DD1 dominates all edges of PPtiti, for ii is odd and all edges in every cycle CCsjsj, jj = 1, ... , tt − 1 and DD2 dominate the edges of PPtiti, for ii is even
IIII ss iiii oooooo aaaaaa tt ≢ 1, in the same manner in the previous case the set DD1 dominates all edges of PPtiti, for ii is odd and all edges in every cycles CCsjsj, jj = 1, ... , tt except one edge in last cycle CCstst
Summary
Let GG = (VV, EE) be a graph with its vertex set VV = VV (GG) and edge set EE = EE(GG). Number” of a graph GG which we denote by γγee(GG) is the minimum cardinality taken over all edge dominating sets of GG.
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