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The vulnerability of the diameter of enhanced hypercubes
For an interconnection network , the {\it -wide diameter}
is the least such that any two vertices are joined by
internally-disjoint paths of length at most , and the {\it
-fault diameter} is the maximum diameter of a
subgraph obtained by deleting fewer than vertices of .
The enhanced hypercube is a variant of the well-known hypercube.
Yang, Chang, Pai, and Chan gave an upper bound for and
and posed the problem of finding the wide diameters and
fault diameters of . By constructing internally disjoint paths between
any two vertices in the enhanced hypercube, for and we
prove
where is the diameter of . These results mean that
interconnection networks modelled by enhanced hypercubes are extremely robust.Comment: 9 pages, 1 figur