图的ni色数的锐界和精确值

IF 0.5 Q4 COMPUTER SCIENCE, THEORY & METHODS

JOURNAL OF INTERCONNECTION NETWORKS Pub Date : 2023-10-20 DOI:10.1142/s021926592350024x

Yangfan Yu, Yuefang Sun

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引用次数: 0

摘要

设[公式:见文本]为连通无向图。如果对于[公式:见文]中的每个顶点[公式:见文]，分配给[公式:见文]的不同颜色的数量最多为[公式:见文]，则[公式:见文]的顶点着色[公式:见文]是[公式:见文]顶点着色。[公式:见文]-[公式:见文]的色数，用[公式:见文]表示，是在一个[公式:见文]-[公式:见文]的顶点着色中使用的最大颜色数。本文对图[公式:见文]的顶点覆盖数、最大度和直径分别给出了[公式:见文]的锐利界。在某些情况下，我们还确定[公式:见文本]的精确值。

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Sharp Bounds and Precise Values for the Ni-Chromatic Number of Graphs

Let [Formula: see text] be a connected undirected graph. A vertex coloring [Formula: see text] of [Formula: see text] is an [Formula: see text]-vertex coloring if for each vertex [Formula: see text] in [Formula: see text], the number of different colors assigned to [Formula: see text] is at most [Formula: see text]. The [Formula: see text]-chromatic number of [Formula: see text], denoted by [Formula: see text], is the maximum number of colors which are used in an [Formula: see text]-vertex coloring of [Formula: see text]. In this paper, we provide sharp bounds for [Formula: see text] of a graph [Formula: see text] in terms of its vertex cover number, maximum degree and diameter, respectively. We also determine precise values for [Formula: see text] in some cases.

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来源期刊

JOURNAL OF INTERCONNECTION NETWORKS COMPUTER SCIENCE, THEORY & METHODS-

自引率

14.30%

发文量

121

期刊介绍： The Journal of Interconnection Networks (JOIN) is an international scientific journal dedicated to advancing the state-of-the-art of interconnection networks. The journal addresses all aspects of interconnection networks including their theory, analysis, design, implementation and application, and corresponding issues of communication, computing and function arising from (or applied to) a variety of multifaceted networks. Interconnection problems occur at different levels in the hardware and software design of communicating entities in integrated circuits, multiprocessors, multicomputers, and communication networks as diverse as telephone systems, cable network systems, computer networks, mobile communication networks, satellite network systems, the Internet and biological systems.