SOME RESULTS ON (p, g,∑)-VALUATION OF GRAPHS
Maryvonne Mahéo, Jean-François Saclé · Discrete Mathematics Algorithms and Applications · 2012
In this article we study proper labelings (or valuations) of the edges of a graph by integers, such that the sums of the values taken on the edges incident to each vertex (the weight of this vertex) are all distinct. We look for the minimum of max (v) among the possible valuations v for some particular classes of graphs.