The k-Total-Proper Index of Graphs

IF 0.5 Q4 COMPUTER SCIENCE, THEORY & METHODS

JOURNAL OF INTERCONNECTION NETWORKS Pub Date : 2023-07-17 DOI:10.1142/s0219265923500111

Ying-zi Ma, Hui Zhang

引用次数: 0

Abstract

Given a set [Formula: see text] with [Formula: see text], a tree [Formula: see text] is considered as a total proper [Formula: see text]-tree or a total proper tree connecting [Formula: see text] if any two adjacent or incident elements of edges and [Formula: see text] of [Formula: see text] differ in color. Let [Formula: see text] be a connected graph of order [Formula: see text], and [Formula: see text] be an integer with [Formula: see text]. A total-colored graph is total proper[Formula: see text]-tree connected if for every set [Formula: see text] of [Formula: see text] vertices, there exists a total proper [Formula: see text]-tree in [Formula: see text]. The [Formula: see text]-total-proper index of [Formula: see text], denoted by [Formula: see text], is the minimum number of colors required to make [Formula: see text] total proper [Formula: see text]-tree connected. In this paper, we first investigate the [Formula: see text]-total-proper index of some special graphs. Moreover, we characterize the graphs with [Formula: see text]-total-proper index [Formula: see text] and [Formula: see text], respectively.

查看原文本刊更多论文

图的k-全固有索引

给定一个集[公式:见文]和[公式:见文]，如果[公式:见文]的边和[公式:见文]的[公式:见文]的[相邻或相关元素]中有任何两个颜色不同，则树[公式:见文]被认为是一个总固有树[公式:见文]或连接[公式:见文]的总固有树。设[公式:见文]为有序的连通图[公式:见文]，[公式:见文]为带[公式:见文]的整数。如果对于[公式:见文本]顶点的每一组[公式:见文本]，在[公式:见文本]中存在一个总固有[公式:见文本]-树，则全彩色图为总固有[公式:见文本]-树连通。[公式:见文]的[公式:见文]-total-proper索引，用[公式:见文]表示，是使[公式:见文]总proper[公式:见文]-树连通所需的最小颜色数。本文首先研究了一些特殊图的[公式:见文]-全-固有索引。此外，我们分别用[公式:见文]-total-proper index[公式:见文]和[公式:见文]来表征图。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.