The Strong Menger Connectivity of the Directed k-Ary n-Cube

IF 0.5 Q4 COMPUTER SCIENCE, THEORY & METHODS

JOURNAL OF INTERCONNECTION NETWORKS Pub Date : 2023-07-19 DOI:10.1142/s0219265923500123

Guoqiang Xie, J. Meng

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引用次数: 0

Abstract

A strong digraph [Formula: see text] is strongly Menger (arc) connected if, for [Formula: see text], [Formula: see text] can reach [Formula: see text] by min[Formula: see text] internally (arc) disjoint-directed paths. A digraph [Formula: see text] is [Formula: see text](-arc)-fault-tolerant strongly Menger([Formula: see text]-(A)FTSM, for short) (arc) connected if [Formula: see text] is strongly Menger (arc) connected for every [Formula: see text](respectively, [Formula: see text]) with [Formula: see text]. A digraph [Formula: see text] is [Formula: see text]-conditional (arc)-fault-tolerant strongly Menger ([Formula: see text]-C(A)FTSM, for short) (arc) connected if [Formula: see text] is strongly Menger (arc) connected for every [Formula: see text](respectively, [Formula: see text]) with [Formula: see text] and [Formula: see text]. The directed [Formula: see text]-ary [Formula: see text]-cube [Formula: see text] [Formula: see text] and [Formula: see text] is a digraph with vertex set [Formula: see text]. For two vertices [Formula: see text] and [Formula: see text], [Formula: see text] dominates [Formula: see text] if there exists an integer [Formula: see text], [Formula: see text], satisfying [Formula: see text]mod [Formula: see text] and [Formula: see text], when [Formula: see text]. In this paper, we show that [Formula: see text] [Formula: see text] is [Formula: see text]-AFTSM arc connected when [Formula: see text], [Formula: see text]-FTSM connected when [Formula: see text], [Formula: see text]-CAFTSM arc connected when [Formula: see text], and [Formula: see text]-CFTSM connected when [Formula: see text].

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有向k-Ary n-立方体的强Menger连通性

一个强有向图[公式:见文]是强门格尔(弧)连通的，如果对于[公式:见文]，[公式:见文]可以通过最小的[公式:见文]内部(弧)不相交的路径到达[公式:见文]。有向图[公式:见文]是[公式:见文](-弧)-容错强门格尔([公式:见文]-(A)FTSM，简称)(弧)连接，如果[公式:见文]与[公式:见文](分别为[公式:见文])是强门格尔(弧)连接。有向图[公式:见文]是[公式:见文]-条件(弧)-容错强门格尔([公式:见文]-C(A)FTSM，简称)(弧)连接，如果[公式:见文]与[公式:见文]和[公式:见文]的每一个[公式:见文](分别为[公式:见文]和[公式:见文])是强门格尔(弧)连接。有向[公式:见文]-ary[公式:见文]-cube[公式:见文][公式:见文]和[公式:见文]是具有顶点集[公式:见文]的有向图。对于两个顶点[公式:见文]和[公式:见文]，如果存在整数[公式:见文]，[公式:见文]，[公式:见文]优于[公式:见文]，满足[公式:见文]mod[公式:见文]和[公式:见文]，当[公式:见文]。在本文中，我们证明了[公式:见文][公式:见文]是[公式:见文]-AFTSM在[公式:见文]时连接，[公式:见文]-FTSM在[公式:见文]时连接，[公式:见文]-CAFTSM在[公式:见文]时连接，[公式:见文]-CFTSM在[公式:见文]时连接。

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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.