A novel edge connectivity based on edge partition for hypercube and folded hypercube

Meirun Chen, Michel Habib, Cheng Kuan Lin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Edge connectivity is often used to capture edge fault tolerance. As for most common networks, their edge connectivity is exactly equal to their minimum degree. Edge matroidal connectivity and conditional edge matroidal connectivity are two new graph edge connectivity parameters that can be defined when a partition of the edge set is given, for example when the network is built with different kinds of edges having different expected faultiness. And those two edge connectivity parameters can measure edge fault tolerance more than the traditional definition. The edge matroidal connectivity is based on the associated edge partition and the other is a generalization called conditional edge matroidal connectivity. We analyze these new parameters on hypercubes and folded hypercubes which are well studied networks. In this study, we consider their standard dimensional partition of the edges. This study leads to more structural insights about edge connectivity and yields many interesting questions.

Original languageEnglish
Article number128558
JournalApplied Mathematics and Computation
Volume470
DOIs
StatePublished - 1 Jun 2024

Keywords

  • Conditional edge matroidal connectivity
  • Edge connectivity
  • Edge matroidal connectivity
  • Faulty edges
  • Folded hypercube
  • Hypercube

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