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Faculty Advisor

T. Kyle Petersen

Abstract

In a proper vertex coloring for a graph G, we call a vertex a b-vertex whenever this vertex is adjacent to at least one vertex of every color class. The b-chromatic number of a graph is defined to be the greatest integer k such that there exists a proper coloring on the graph with k colors where there is at least one b-vertex in every color class. This paper is on the b-chromatic number of the total graphs of complete bipartite graphs. We find bounds of the b-chromatic number for the total graphs of complete bipartite graphs and provide a method to calculate the b-chromatic number of the total graphs of complete bipartite graphs in specific conditions.

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