Quantum Probability Aspects to Lexicographic and Strong Products of Graphs

Nobuaki OBATA

doi:10.4036/iis.2016.S.01

Interdisciplinary Information Sciences

Online ISSN : 1347-6157
Print ISSN : 1340-9050
ISSN-L : 1340-9050

This article has now been updated. Please use the final version.

Quantum Probability Aspects to Lexicographic and Strong Products of Graphs

Nobuaki OBATA

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Keywords: adjacency matrix, convolution of probability distributions, lexicographic product, spectral distribution, strong product

JOURNAL FREE ACCESS Advance online publication

Article ID: 2016.S.01

DOI https://doi.org/10.4036/iis.2016.S.01

The final version of this article is now available: Vol. 22 (2016), No. 1 pp. 143-146

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Abstract

The adjacency matrix of the lexicographic product of graphs is decomposed into a sum of monotone independent random variables in a certain product state. The adjacency matrix of the strong product of graphs is decomposed into a sum of commutative independent random variables in a product state. Their spectral distributions are obtained by using the monotone, classical and Mellin convolutions of probability distributions.

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