The 3-Wide-Diameter of the Hyper-L Triple-Loop Network

The wide-diameter of a network has been considered as an important measurement of fault-tolerance. The 3-wide-diameter of a network is defined as the minimum length l such that, between any two nodes, there are three disjoint paths of length at most l. With small diameter D and simple structure, the hyper-L triple-loop network, denoted by HL(l, m, n), has been showed to be a good construction for a triple-loop network. Hwang and Lin proved that the 3-wide-diameter of hyper-L triple-loop network is at most D + 2. In this paper, we exactly present the S-wide-diameter of hyper-L triple-loop network. We prove that the 3-wide-diameter is D + 1 except two cases with D + 2