Research on the Diameter and Average Diameter of Undirected Double-loop Networks

As the diameter of an undirected double-loop network represents its maximum transmission delay of information, the average diameter of an undirected double-loop network represents its average transmission delay of information. However, up to now the diameter has been received much more emphasis than the average diameter. A method to calculate the diameter as well as the average diameter is proposed. It is found out that, (a) for some fixed there may exist several tight-optimal undirected double-loop networks, but their average diameters may not reach the same minimum value, (b) for some fixed N the average diameters of their tight-optimal undirected double-loop networks are not smaller than those of their 1-tight even 2-tight optimal undirected double-loop networks. These findings tell us that an undirected double-loop network may have an optimal diameter but has not an optimal average diameter, so not only the diameter but also the average diameter should be taken into account in designing an optimal double-loop network. An undirected double-loop network with an optimal diameter and an optimal average diameter is defined as a dual-optimal double-loop network.