Asymptotic spectral distributions
of distance-$k$ graphs of Cartesian product graphs
Colloquium Mathematicum, Tome 132 (2013) no. 1, pp. 35-51
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Let $G$ be a finite connected graph on two or more vertices, and $G^{[N,k]}$ the distance-$k$ graph of the $N$-fold Cartesian power of $G$. For a fixed $k\ge 1$, we obtain explicitly the large $N$ limit of the spectral distribution (the eigenvalue distribution of the adjacency matrix) of $G^{[N,k]}$. The limit distribution is described in terms of the Hermite polynomials. The proof is based on asymptotic combinatorics along with quantum probability theory.
Keywords:
finite connected graph vertices distance k graph n fold cartesian power fixed obtain explicitly large limit spectral distribution eigenvalue distribution adjacency matrix limit distribution described terms hermite polynomials proof based asymptotic combinatorics along quantum probability theory
Affiliations des auteurs :
Yuji Hibino 1 ; Hun Hee Lee 2 ; Nobuaki Obata 3
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author = {Yuji Hibino and Hun Hee Lee and Nobuaki Obata},
title = {Asymptotic spectral distributions
of distance-$k$ graphs of {Cartesian} product graphs},
journal = {Colloquium Mathematicum},
pages = {35--51},
publisher = {mathdoc},
volume = {132},
number = {1},
year = {2013},
doi = {10.4064/cm132-1-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm132-1-4/}
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Yuji Hibino; Hun Hee Lee; Nobuaki Obata. Asymptotic spectral distributions of distance-$k$ graphs of Cartesian product graphs. Colloquium Mathematicum, Tome 132 (2013) no. 1, pp. 35-51. doi: 10.4064/cm132-1-4
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