Other Mathematics Commons^™

Sum-Defined Colorings In Graphs, James Hallas

Honors Theses

There have been numerous studies using a variety of methods for the purpose of uniquely distinguishing every two adjacent vertices of a graph. Many of these methods have involved graph colorings. The most studied colorings are proper colorings. A proper coloring of a graph G is an assignment of colors to the vertices of G such that adjacent vertices are assigned distinct colors. The minimum number of colors required in a proper coloring of G is the chromatic number of G. In our work, we introduce a new coloring that induces a (nearly) proper coloring. Two vertices u and …