Comments on "Low Diameter Interconnections for Routing in High-Performance Parallel Systems, " with Connections and Extensions to Arc Coloring of Coset Graphs

Recently, Melhem presented a ”new” class of low-diameter interconnection (LDI) networks in this journal [10]. We note that LDI networks are the same as the previously known generalized de Bruijn graphs, point out an error in the decomposition of LDI networks into permutations, and find that the correct decomposition scheme is an instance of arc coloring for coset graphs. Hence, we pursue a number of general results on arc coloring of coset graphs that can be applied to this particular decomposition problem as well as within many other contexts, including complete arc coloring and normality of coset graphs.