TY  - THES
T1  - Chromatic Equivalence Classes and Chromatic Defining Numbers of Certain Graphs
A1  - Omoomi, Behnaz
LA  - English
YR  - 2001
UL  - http://discoverylib.upm.edu.my/discovery/Record/oai:ethesis.upm.edu.my:3532
AB  - 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.
ER  -