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

Date of Publication

2016

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics with specialization in Business Applications

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Thesis Adviser

Leonor Aquino Ruivivar

Abstract/Summary

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.

Abstract Format

html

Language

English

Format

Electronic

Accession Number

CDTU020972

Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

Physical Description

1 computer disc ; 4 3/4 in.

Keywords

Graph theory, Colors--Analysis

Embargo Period

5-11-2021

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