Asymptotic spectral distributions of distance-k graphs of Cartesian product graphs

• Autorzy: Yuji Hibino , Hun Hee Lee , Nobuaki Obata
• Języki publikacji: EN

Abstrakty

EN

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 ≥ 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.

Kategorie tematyczne

• 05C12: Distance in graphs
• 81S25: Quantum stochastic calculus
• 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.)
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 132
• Numer: 1
• Strony: 35-51

Daty

wydano

2013

Twórcy

autor

Yuji Hibino

• Department of Mathematics, Saga University, Saga, 840-8502, Japan

autor

Hun Hee Lee

• Department of Mathematical Sciences and, Research Institute of Mathematics, Seoul National University, Seoul 151-747, Republic of Korea

autor

Nobuaki Obata

• Graduate School of Information Sciences, Tohoku University, Sendai, 980-8579, Japan

Identyfikatory

DOI

10.4064/cm132-1-4