As the scales of multiprocessor systems expand, the demand for high reliability and security grows proportionally. Network topology (or graph) modeling, which maps the interconnection patterns between processors and links in a multiprocessor system, serves as an effective methodology for investigating system reliability. Among various network robustness metrics, connectivity is a critical evaluation criterion. H-(sub)structure connectivity is a generalization of traditional connectivity, and numerous studies have been conducted the fault tolerability of to evaluate various networks. As an extended variant of the hypercube, the exchanged crossed cube combines the advantages of smaller diameter and fewer edges. These advantages enable the network to achieve lower hardware costs while maintaining more efficient data transmission. In this paper, we investigate the H-(sub)structure connectivity of the exchanged crossed cube ECQ(s, t) when H is isomorphic to <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11227_2025_7866_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">$P_k$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mi>k</mi> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11227_2025_7866_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">$C_k$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mi>k</mi> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11227_2025_7866_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="32" /> </InlineMediaObject> <EquationSource Format="TEX">$K_{1, r}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>K</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>r</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>.

Fault tolerance assessment of exchanged crossed cube based on structure fault pattern

期刊论文
发表日期：

2025年10月8日

查看全文

Xiaowang Li,
Lili Tian,
Shuming Zhou,
Leyi Jia,
Zihan Shi

摘要

As the scales of multiprocessor systems expand, the demand for high reliability and security grows proportionally. Network topology (or graph) modeling, which maps the interconnection patterns between processors and links in a multiprocessor system, serves as an effective methodology for investigating system reliability. Among various network robustness metrics, connectivity is a critical evaluation criterion. H-(sub)structure connectivity is a generalization of traditional connectivity, and numerous studies have been conducted the fault tolerability of to evaluate various networks. As an extended variant of the hypercube, the exchanged crossed cube combines the advantages of smaller diameter and fewer edges. These advantages enable the network to achieve lower hardware costs while maintaining more efficient data transmission. In this paper, we investigate the H-(sub)structure connectivity of the exchanged crossed cube ECQ(s, t) when H is isomorphic to $P_k$ $P_{k}$ , $C_k$ $C_{k}$ and $K_{1, r}$ $K_{1, r}$ .