Graph coloring is an important concept in graph theory. A totally silver coloring of a graph G is a k - coloring of G such that for every vertex v V ( G ), each color appears exactly once in N [ v ], the closed neighborhood of v . A totally silver graph is a graph which admits a totally silver coloring.Totally silver coloring are directly related to other areas of graph theory such as distance coloring and domination. In this thesis, we present several constructive characterizations of totally silver graphs and give several infinite families of these graphs.
