Vertex coloring of graphs by total 2-weightings
by
Jonathan Hulgan
University of Memphis
Coauthors: Jeno Lehel (University of Memphis) Kenta Ozeki (Keio University) Kiyoshi Yoshimoto (Nihon University)

An assignment of real weights to the edges and the vertices of a graph is a vertex-coloring total weighting if the total weight sums at the vertices are distinct for any two adjacent vertices. Of interest in this paper is the existence of vertex-coloring total weightings with weight set of cardinality two, a problem motivated by the conjecture that every graph has a such a weighting using the weights 1 and 2. Here we prove the existence of such weightings for certain families of graphs using any two distinct non-negative real weights.

Date received: April 3, 2009