# Asymptotic spectral distributions of Manhattan products of $$C_{n}\sharp P_{m}$$ C n ♯ P m

Asymptotic spectral distributions of Manhattan products of $$C_{n}\sharp P_{m}$$ C n ♯ P m The Manhattan product of directed cycles $$C_{n}$$ C n and directed paths $$P_{m}$$ 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- $$C_{n}\sharp P_{m}$$ C n ♯ P m . The limit of the spectral distribution of $$C_{n}\sharp P_{2}$$ C n ♯ P 2 as $$n\rightarrow \infty$$ n → ∞ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Asymptotic spectral distributions of Manhattan products of $$C_{n}\sharp P_{m}$$ C n ♯ P m

, Volume 13 (11) – Aug 15, 2014
13 pages

/lp/springer_journal/asymptotic-spectral-distributions-of-manhattan-products-of-c-n-sharp-p-A3zUaleMeU
Publisher
Springer US
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-014-0804-0
Publisher site
See Article on Publisher Site

### Abstract

The Manhattan product of directed cycles $$C_{n}$$ C n and directed paths $$P_{m}$$ 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- $$C_{n}\sharp P_{m}$$ C n ♯ P m . The limit of the spectral distribution of $$C_{n}\sharp P_{2}$$ C n ♯ P 2 as $$n\rightarrow \infty$$ n → ∞ 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.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Aug 15, 2014

### References

• Spectra of digraphs
Brualdi, RA
• The spectra of Manhattan street networks
Comellas, F; Dalfo, C; Fiol, MA; Mitjana, M

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