Some Bounds on the Nonnegative Signed Edge Domination Number in graph s

Let G = (V,E) be a simple graph. The function f : E(G)-1,1} is a non-negative signed edge dominating function (NNSEDF) if for every edge eε E(G) , f x . The value of f f e is called the weight of f . The nonnegative signed edge domination number of G is the minimum weight of a nonnegative signed edge dominating function of G . In this paper, we initiate the study of the nonnegative signed edge domination numbers and we find some lower and upper bounds for this parameter. We also calculate the exact value of the nonnegative signed edge domination number of graph G , when it is a star, a wheel, a fan, a Dutch windmill, a cycle, a path, a complete (n 1) -regular or a complete bipartite graph.