Some Results On Total Onto Minus Edge Dominating Functions In Graphs

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.