On the locating-chromatic number of some classes of graphs and graphs obtained from graph operations

• Main Authors: Orgasan, Jude Ezekiel M., Tacub, Carmela Joy C.
• Format: text
• Language: English
• Published: Animo Repository 2016
• Subjects: Graph theory, Colors > Analysis; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/14918
• Institution: De La Salle University

Let G = (V E) be a graph. Let c be a proper k-coloring of a connected graph G and = fC1 C2 : : : Cng be an ordered partition of V (G) induced from the coloring c resulting into color classes. For a vertex v 2 V (G), the color code of v with respect to is de ned as the ordered k-tuple c (v) = (d(v C1) d(v C2) : : : d(v Ck)) where d(v Ci) = minfd(v u) : u 2 Cig for i = 1 2 : : : k. If every vertex in G has distinct color codes, then c is called a locating coloring. The minimum positive integer k for which G has a locating coloring is called the locating-chromatic number of G, denoted by L(G).In this paper, we determine the locating-chromatic number of some common classes of graphs. We also investigate the locating-chromatic number of powers of some graphs. Moreover, we provide a partial exposition on studies involving the locating-chromatic number of graphs resulting from graph operations such as cartesian products, joins and corona products of graphs.