Circulant graphs and tessellations on flat tori
type: Item
instance of: scholarly article
title: Circulant graphs and tessellations on flat tori
zbMATH Open document ID: 1211.52016
author: T. B. Carlos
author: Sueli I. R. Costa
author: João E. Strapasson
author: Marcelo M. S. Alves
published in: Linear Algebra and its Applications
publication date: 2009-12-18T00:00:00Z
review text: Circulant graphs are here considered as the vertices and edges of a tesselation of a \(k\)-dimensional torus by hypercubes. Conditions are provided for a quotient lattice to give rise to a circulant graph on flat torus, and it is shown that any circulant graph can be embedded in a flat torus. It is also proved via this geometrical interpretation that to each circulant graph with maximum density there corresponds a perfect code in the Lee space.
reviewed by: Dragan Stevanović
Mathematics Subject Classification ID: 52C07
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 94B05
zbMATH DE Number: 5650047
zbMATH Keywords: circulant graphs
zbMATH Keywords: graphs on flat tori
zbMATH Keywords: genus of circulant graphs
zbMATH Keywords: lattices
zbMATH Keywords: Lee codes
MaRDI profile type: Publication
full work available at URL: j.laa.2009.08.040
OpenAlex ID: W1985561734
cites work: On planarity and colorability of circulant graphs
cites work: The Degree-Diameter Problem for Several Varieties of Cayley Graphs I: The Abelian Case
cites work: Circulant graph imbeddings
cites work: Q5556894
cites work: On perfect Lee codes
cites work: Graphs with circulant adjacency matrices
cites work: Counting circulant graphs of prime-power order by decomposing into orbit enumeration problems
cites work: Ádám's conjecture is true in the square-free case
cites work: Circulants and their connectivities
cites work: Geometry of surfaces
cites work: Graphs, Tessellations, and Perfect Codes on Flat Tori
cites work: Q4219187
cites work: Q5441582
cites work: Q4705771
cites work: Quasi-perfect Lee distance codes
cites work: Topological graph theory.
cites work: On the algebraic connectivity of graphs as a function of genus
DOI: 10.1016/J.LAA.2009.08.040
description: scientific article; zbMATH DE number 5650047