Component Edge Connectivity of Hypercube-like Networks

TL;DR

This paper investigates the g-component edge connectivity of hypercube-like networks, a class of interconnection networks derived from hypercubes, providing exact connectivity measures for these complex structures.

Contribution

It determines the (g+1)-component edge connectivity of n-dimensional hypercube-like networks, extending understanding of their robustness and fault tolerance.

Findings

Exact (g+1)-component edge connectivity values for HL-networks

Extension of connectivity concepts to hypercube-like structures

Insights into fault tolerance of interconnection networks

Abstract

As a generalization of the traditional connectivity, the g-component edge connectivity c{\lambda}g(G) of a non-complete graph G is the minimum number of edges to be deleted from the graph G such that the resulting graph has at least g components. Hypercube-like networks (HL-networks for short) are obtained by manipulating some pairs of edges in hypercubes, which contain several famous interconnection networks such as twisted cubes, Mobius cubes, crossed cubes, locally twisted cubes. In this paper, we determine the (g + 1)-component edge connectivity of the n-dimensional HL-networks.