Abstract
Let G = (V, E) be a graph. The total onto minus edge dominating function is a function f: E → {−1, 0, 1} such that f is onto and f (N(e)) ≥ 1 for all e ∈ E(G). The total onto minus edge domination number of a graph G is a minimum weight of a set of all total onto minus edge dominating functions of G and it is denoted by .
 In this paper we discuss about the total onto minus edge domination number for some graphs : Star graph, Bistar graph, Friendship graph and Flower graph.
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