derived graphs — 1 articles found.

Laplacians for Derived Graphs of Regular Kähler Graphs

C. R. Math. Rep. Acad. Sci. Canada Vol. 37 (4) 2015, pp. 142-157
Vol.37 (4) 2015
Yaermaimaiti Tuerxunmaimaiti; Toshiaki Adachi Details
(Received: 2014-07-13 , Revised: 2015-07-15 )
(Received: 2014-07-13 , Revised: 2015-07-15 )

Yaermaimaiti Tuerxunmaimaiti,Division of Mathematics and Mathematical Science, Nagoya Institute of
Technology, Nagoya 466-8555, Japan; e-mail: yarimamat@gmail.com

Toshiaki Adachi,Department of Mathematics, Nagoya Institute of Technology, Nagoya 466-8555, Japan; e-mail: adachi@nitech.ac.jp

Abstract/Résumé:

We consider \((p,q)\)-step adjacency on a Kähler graph which is compounded from a principal graph and an auxiliary graph. We attach probabilistic weights to \((p,q)\)-step paths so that these paths show trajectories under the influence of a magnetic field of strength \(q/p\) on this graph. We study eigenvalues of Laplacians corresponding to \((p,q)\)-step paths on some regular Kähler graphs and give examples of pairs of regular Kähler graphs whose Laplacians for arbitrary pairs \((p,q)\) of positive integers have the same eigenvalues.

On considère la relation de contiguité à un pas \((p,q)\) près sur un graphe kählerien qui se constitue d’un graphe principal et un graphe auxiliaire. On attache des poids probabilistiques aux sentiers dans un tel graphe composés de pas \((p,q)\) de sorte que ces sentiers montrent des trajectoires sous l’influence d’un champs magnétique de force \(q/p\) sur le graphe. On étudie le spectre de l’opérateur laplacien correspondant aux sentiers aux pas \((p,q)\) sur certains graphes kähleriens regulières. On donne un example de deux graphes différents dont les opérateurs laplaciens ont le même spectre pour toute paire \((p,q)\).

Keywords: (p; q)-Laplacians, Kähler graphs, complement graphs, derived graphs, isospectral, products of graphs

AMS Subject Classification: Graphs and matrices, Hermitian and K_õhlerian manifolds 05C50, 53C55

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