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We present a local broadcasting schema for the multidimensional mesh structures, which will transmit a message to <i>all the nodes</i> within the minimal amount of time. We will also study the average amount of time it takes for such a schema to send a message to an arbitrary but fixed node in the structure.
We provide general techniques to estimate an upper bound of the conditional diag-nosability of a graph G, and to prove that such a bound is also tight when a certain connectivity result is available for G. As an example, we derive the exact value of the conditional diagnosability for the (n, k)-star graph.
The class of alternating group networks was introduced in the late 1990’s as an alternative to the alternating group graphs as interconnection networks. Recently, additional properties for the alternating group networks have been published. In particular, Zhou et al., J. Supercomput (2009), doi: 10.1007/s11227-009-0304-7 , was published very recently in… (More)