Abstract
Abstract 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], Konig [7], and Nordhaus-Gaddum type inequalities will be presented.
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