The Wide Diameter and Fault Diameter of Exchanged Crossed Cube

Abstract

The fault diameter and wide diameter are commonly used to measure the fault tolerance and transmission delay of interconnection networks beyond traditional diameter. The [Formula: see text]-wide diameter of graph [Formula: see text], denoted by [Formula: see text], is the minimum integer [Formula: see text] such that there exist at least [Formula: see text] internally vertex disjoint paths of length at most [Formula: see text] for any two distinct vertices in [Formula: see text]. The [Formula: see text]-fault diameter of graph [Formula: see text], denoted by [Formula: see text], is the maximum diameter of the survival graph obtained by deleting at most [Formula: see text] vertices in [Formula: see text]. The exchanged crossed cube, as a compounded interconnection network denoted by [Formula: see text], holds the desirable properties of both crossed cube and exchanged hypercube, while achieving a better balanced between cost and performance of the parallel computing systems. In this paper, we construct [Formula: see text] internally vertex disjoint paths between any two distinct vertices of [Formula: see text]. Moreover, we determine the upper and lower bounds of [Formula: see text]-wide diameter and [Formula: see text]-fault diameter of [Formula: see text], i.e., [Formula: see text], which shows that the exchanged crossed cube has better efficiency and reliability than that of the exchanged hypercube.