交叉立方体的广义3-连通性和4-连通性

IF 0.5 4区数学 Q3 MATHEMATICS

Discussiones Mathematicae Graph Theory Pub Date : 2022-11-18 DOI:10.7151/dmgt.2474

Heqin Liu, Dongqin Cheng

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引用次数: 1

摘要

广义连通性是连通性的一种扩展，为网络容错能力的测量提供了新的参考。对任意连通图G，令S≤|S|≤V (G);κG(S)是连接S的G中内部不相交树的最大个数。G的广义k-连通性，κk(G)被定义为κG(S)在所有S的 V (G)上的最小值，且|S| = k。n维交叉立方体CQn作为一种超立方体网络，由于其许多良好的性质，被认为是超立方体网络的一种有吸引力的替代方案。研究了CQn的广义3-连通性和广义4-连通性，得到了κ3(CQn) = κ4(CQn) = n−1，其中n≥2。

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The Generalized 3-Connectivity and 4-Connectivity of Crossed Cube

Abstract The generalized connectivity, an extension of connectivity, provides a new reference for measuring the fault tolerance of networks. For any connected graph G, let S ⊆ V (G) and 2 ≤ |S| ≤ V (G); κG(S) refers to the maximum number of internally disjoint trees in G connecting S. The generalized k-connectivity of G, κk(G), is defined as the minimum value of κG(S) over all S ⊆ V (G) with |S| = k. The n-dimensional crossed cube CQn, as a hypercube-like network, is considered as an attractive alternative to hypercube network because of its many good properties. In this paper, we study the generalized 3-connectivity and the generalized 4-connectivity of CQnand obtain κ3(CQn) = κ4(CQn) = n − 1, where n ≥ 2.

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来源期刊

Discussiones Mathematicae Graph Theory MATHEMATICS-

CiteScore

2.20

自引率

0.00%

发文量

审稿时长

53 weeks

期刊介绍： The Discussiones Mathematicae Graph Theory publishes high-quality refereed original papers. Occasionally, very authoritative expository survey articles and notes of exceptional value can be published. The journal is mainly devoted to the following topics in Graph Theory: colourings, partitions (general colourings), hereditary properties, independence and domination, structures in graphs (sets, paths, cycles, etc.), local properties, products of graphs as well as graph algorithms related to these topics.