Chromatic Equivalence Classes and Chromatic Defining Numbers of Certain Graphs

Omoomi, Behnaz (2001) Chromatic Equivalence Classes and Chromatic Defining Numbers of Certain Graphs. PhD thesis, Universiti Putra Malaysia.

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Abstract

There are two parts in this dissertation: the chromatic equivalence classes and the chromatic defining numbers of graphs. In the first part the chromaticity of the family of generalized polygon trees with intercourse number two, denoted by Cr (a, b; c, d), is studied. It is known that Cr( a, b; c, d) is a chromatic equivalence class if min {a, b, c, d} ≥ r+3. We consider Cr( a, b; c, d) when min{ a, b, c, d} ≤ r + 2. The necessary and sufficient conditions for Cr(a, b; c, d) with min {a, b, c, d} ≤ r + 2 to be a chromatic equivalence class are given. Thus, the chromaticity of Cr (a, b; c, d) is completely characterized. In the second part the defining numbers of regular graphs are studied. Let d(n, r, X = k) be the smallest value of defining numbers of all r-regular graphs of order n and the chromatic number equals to k. It is proved that for a given integer k and each r ≥ 2(k - 1) and n ≥ 2k, d(n, r, X = k) = k - 1. Next, a new lower bound for the defining numbers of r-regular k-chromatic graphs with k < r < 2( k - 1) is found. Finally, the value of d( n , r, X = k) when k < r < 2(k - 1) for certain values of n and r is determined.

Item Type:Thesis (PhD)
Subject:Chromatographic analysis
Chairman Supervisor:Associate Professor Peng Vee Hock, PhD
Call Number:FSAS 2001 57
Faculty or Institute:Faculty of Science and Environmental Studies
ID Code:9335
Deposited By: Tuan Norasiah Tuan Yaacob
Deposited On:24 Jan 2011 03:00
Last Modified:30 Sep 2013 07:10

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