A total edge dominating set of a graph is a set of edges of such that the sub graph has no isolated edges. The total edge domination number of denoted by, is the minimum cardinality of a total edge dominating set of. Further, the set is said to be double edge dominating set of graph. If every edge of is dominated by at least two edges of. The double edge domination number of, denoted by, , is the minimum cardinality of a double edge dominating set of . In this paper, we provide a constructive characterization of trees with equal total edge domination and double edge domination numbers.
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