Some results on graph parameters in weighted graphs

A weighted graph (G,w) is a graph G = (V(G),E(G)) together with a real-valued weight-function on its vertices w : V(G) → R. We will define and study generalizations of the matching number, the edge covering number and the domination number for weighted graphs. Generalizations of well-known theorems due to Gallai [5], König [7], and Nordhaus-Gaddum type inequalities will be presented.