FRACTIONAL EDGE DOMINATION IN GRAPHS

Let G = (V,E) be a graph. A function f : E -> [0,1] is called an edge dominating function if Sigma(x is an element of N[e]) f(x) >= 1 for all e is an element of E(G), where N[e] is the closed neighbourhood of the edge e. An edge dominating function f is called minimal (MEDF) if for all functions g : E -> [0,1] with g < f, g is not an edge dominating function. The fractional edge domination number gamma'(f) and the upper fractional edge domination number Gamma'(f) are defined by gamma'f (G) = min{vertical bar f vertical bar : f is an MEDF of G} and Gamma'f (G) = max{vertical bar f vertical bar : f is an MEDF of G}, where vertical bar f vertical bar = Sigma(e is an element of E) f(e). Further we introduce the fractional parameters corres ponding to edge irredundance and edge in dependence, leading to the fract ional edge domination chain. We also consider topological properties of the set of all edge dominating functions of G.