Asymptotic spectral distributions of Manhattan products of C-n#P-m

作者：Kang Yuanbao^*; Wang Caishi

来源：Quantum Information Processing, 2014, 13(11): 2499-2511.

DOI：10.1007/s11128-014-0804-0

• Asymptotic spectral distribution
• Manhattan products of the digraphs
• The limit of the spectral distribution

The Manhattan product of directed cycles C-n and directed paths P-m is a diagraph. Recently, in quantum probability theory, several authors have studied the spectrum of graph, as mentioned also by A. Hora and N. Obata. In the paper, we study asymptotic spectral distribution of the Manhattan products of simple digraphs-C-n # P-m. The limit of the spectral distribution of C-n # P-2 as n -> infinity exists in the sense of weak convergence, and its concrete form is obtained. We insist on the fact that this note does not contain any new results, which is only some parallel results with Obata (Interdiscip Inf Sci 18(1):43-54, 2012) or Obata (Ann Funct Anal 3:136-144, 2012). But, we have only been written to convey the information from quantum probability to spectral analysis of graph.

• 出版日期2014-11
• 单位西北师范大学