The Locating Chromatic Number of a Disjoint Union of Some Double Stars

Abstract

In this paper we discuss the locating chromatic number of a disconnected graph, namely a disjoint union of some double stars. To determine the locating-chromatic number of a graph, first we construct the upper bound of the number and observe the minimum coloring used. Then, to determine the lower bound of the number, we use the trivial lower bound for some leaves which incident to one vertex. Two main theorems about the locating chromatic number of a disjoint union of some double stars. We obtained some original results of the locating chromatic number of disjoint union of some double stars. Moreover, we can generalize the graph such that the locating chromatic number remains the same with the previous one.