Fault Diameter of Hypercubes With Hybrid Node and Link Faults

Abstract

In this paper we study the fault diameter of the n-dimensional hypercube (or n-cube for short), Qn, for n ≥ 3. Let F be a set of hybrid node-faults and/or link-faults in Qn such that every node of Qn is still connected to at least one fault-free node by a fault-free link. Then we compute the exact diameter of Qn - F for |F| ≤ 2n - 3. As an immediate consequence, our result improves upon those presented by S. Latifi (1993), in which only node-faults were addressed.

The vulnerability of the diameter of the enhanced hypercubes

“…These parameters were studied by several authors for some Cartesian product graphs [7,25,26] and for the hypercube and its variants [3,5,8,10,18,19,20].…”

“…They combine connectivity with diameter to measure simultaneously the fault-tolerance and efficiency of parallel processing computer networks. These parameters were studied by several authors for some Cartesian product graphs [7,25,26] and for the hypercube and its variants [3,5,8,10,18,19,20].…”

Topological properties on the diameters of the integer simplex

“…The parameters of some well-known networks such as hypercube, crossed cube etc. were studied in [4,5,9,11,12,15,18].…”

Conditional Fault Diagnosability of Dual-Cubes

“…As the number of faults in the graph is increased, it is desirable that the most part of the surviving network retain connection, with a few processors separated from the rest, since then the network will continue to be able to function. Many interconnection networks have been investigated in this aspect, when the number of faults is roughly twice the connectivity, see [12,24]. One can even go further and ask what happens when more faulty vertices appear.…”