Abstract
The double loop networkG(N;r,s) hasN vertices and2N directed edges. A natural question is how to chooser ands such thatG(N;r,s) has diameter as short as possible for a givenN. In 1993, Li, Xu and Zhang proposed a method of constructing double loop networks with the minimum diameter for the case ofr=1. The method is developed to construct such networks that none of their minimum diameters can be reached atr=1. As a by-product, a flaw in an assertation by Esque et al. is pointed out.
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