The minimum covering energy ܧ )ܩ( and minimum dominating energy ܧ )ܩ( of a graph are well known problems of graph theory. Motivated by the work of [1,7] and also by similar works, in this paper, we introduced minimum total edge dominating energy ܧ ாௗ )ܩ( of a Graph is introduced. Minimum total edge dominating energy of a Star Graph and complete graph is computed.
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