Structure Connectivity and Substructure Connectivity of Alternating Group Graphs

Lantao You, Yuejuan Han, Xi Wang, Chen Zhou, Rui Gu, Chen Lu
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引用次数: 5

Abstract

The alternating group graph, denoted by AGn, is one of the popular interconnection networks. In this paper, we consider two network connectivities, H-structure-connectivity and H-substructure-connectivity, which are new measures for a network’s reliability and fault-tolerability. We say that a set F of connected subgraphs of G is a subgraph-cut of G if G−V (F) is a disconnected or trivial graph. Let H be a connected subgraph of G. Then F is an H-structure-cut, if F is a subgraph-cut, and every element in F is isomorphic to H. And F is an H-substructure-cut if F is a subgraph-cut, such that every element in F is isomorphic to a connected subgraph of H. The H-structure-connectivity(resp. H-substructure-connectivity) of G, denoted by κ(G;H)(resp. κs(G;H)), is the minimum cardinality of all H-structure-cuts(resp. H-substructure-cuts) of G. In this paper, we will establish both κ(AGn;H) and κ(AGn;H) for the alternating group graph AGn and H ∈{K1,K1,1,K1,2}.
交替群图的结构连通性和子结构连通性
交替群图是一种常用的互连网络,用AGn表示。本文考虑了两种网络连通性:h结构连通性和h子结构连通性,它们是衡量网络可靠性和容错性的新指标。如果G−V (F)是一个不连通图或平凡图,我们说G的连通子图集合F是G的子图切。设H是g的连通子图,则F是H结构切,如果F是子图切,且F中的每个元素与H同构;如果F是子图切,使得F中的每个元素与H的连通子图同构,则F是H结构切。G的H-子结构-连通性),用κ(G;H)表示。κs(G;H)),是所有H结构切割的最小基数。本文将建立交替群图AGn和H∈{K1,K1,1,K1,2}的κ(AGn;H)和κ(AGn;H)。
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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