The Neighbor Locating Chromatic Number of Some Graphs

Abstract

Let G = (V, E) be a simple graph. A proper vertex coloring of G consists in assigning a color to each vertex of G so that two adjacent vertices are colored differently. The minimum number of colors in a proper coloring of vertex of G is called the chromatic number. A neighbor locating coloring is a coloring where any two distinct vertices belonging to the same color class can be distinguished from each other by the colors of their respective neighbors. The minimum cardinality of a neighbor locating coloring of G is the neighborhood locating chromatic number. Throughout the dissertation, we study the neighbor locating chromatic number and we provide results on the neighbor locating chromatic number of some special graphs, namely, the total graph of the star and wheel graphs and the book graphs