On the existence of hyper-L triple-loop networks

Aguiló-Gost [New dense families of triple loop Networks, Discrete Math. 197/198 (1999) 15–27] has presented a new type of hyper-L tiles and used it to derive a new dense family of triple-loop networks. While Aguiló-Gost's hyper-L tile seems to be a promising tool for studying the triple-loop networks, we need to verify that the hyper-L tile producing good result is indeed the MDD of some triple-loop network. In this paper, we give necessary and sufficient conditions for the existence of Aguiló-Gost's hyper-L triple-loop networks and we correct some flaws in [F. Aguiló-Gost, New dense families of triple loop networks, Discrete Math. 197/198 (1999) 15–27].