The Distinguishing Chromatic Number
The Distinguishing Chromatic Number
复制标题
区分色数
DOI：
10.37236/1042
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
Ann N. Trenk
中科院分区：
文献类型：
--
作者：
Karen L. Collins;Ann N. Trenk
本文在Albertson和Collins研究图$G$的可分辨色数的基础上，定义并研究了图$G$的可分辨色数$\chi_D(G)$。我们找到了各种图族的$\chi_D(G)$，并用$\chi_D(G)$ = |V(G)|$和树的最大色区分数刻画了这些图。我们证明了布鲁克斯定理对可分辨数和可分辨色数，以及对树和连通图的类似性质。我们最后作了一些推测。
In this paper we define and study the distinguishing chromatic number, $\chi_D(G)$, of a graph $G$, building on the work of Albertson and Collins who studied the distinguishing number. We find $\chi_D(G)$ for various families of graphs and characterize those graphs with $\chi_D(G)$ $ = |V(G)|$, and those trees with the maximum chromatic distingushing number for trees. We prove analogs of Brooks' Theorem for both the distinguishing number and the distinguishing chromatic number, and for both trees and connected graphs. We conclude with some conjectures.
DOI：
10.5860/choice.42-2854b
发表时间：
2007-04
期刊：
--
影响因子：
--
作者：
J. Gross
通讯作者：
J. Gross