关于若干环相关图的δ(k)-着色

IF 0.5 Q4 COMPUTER SCIENCE, THEORY & METHODS

JOURNAL OF INTERCONNECTION NETWORKS Pub Date : 2023-08-08 DOI:10.1142/s0219265923500147

Merlin Thomas Ellumkalayil, S. Naduvath

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引用次数: 0

摘要

当相邻的一对顶点的颜色不同时，图形的上色是正确的，当相邻的一对顶点中至少有一个接收到相同的颜色时，图形的上色是不正确的。当对图形进行适当着色所需的最小颜色数量不可用时，用可用的颜色(例如[公式:见文本]颜色)对图形进行着色，将导致至少一条边的端点具有相同的颜色。这样的边叫做坏边。在图的适当着色中[公式:见文本]，每个颜色类都是一个独立的集合。然而，在不正确的着色中，可能会有几个非独立的颜色类。在本文中，我们使用了[公式:见文]-着色的概念，它只允许一个颜色类是非独立的，并确定了坏边的最小数量，用[公式:见文]表示，这是由相同的方法得到的一些与循环相关的图。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On δ(k)-Coloring of Some Cycle-Related Graphs

A graph coloring is proper when the colors assigned to a pair of adjacent vertices in it are different and it is improper when at least one of the adjacent pair of vertices receives the same color. When the minimum number of colors required in a proper coloring of a graph is not available, coloring the graph with the available colors, say [Formula: see text] colors, will lead at least an edge to have its end vertices colored with a same color. Such an edge is called a bad edge. In a proper coloring of a graph [Formula: see text], every color class is an independent set. However, in an improper coloring there can be few color classes that are non-independent. In this paper, we use the concept of [Formula: see text]-coloring, which permits only one color class to be non-independent and determine the minimum number of bad edges, which is denoted by [Formula: see text], obtained from the same for some cycle-related graphs.

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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.