On congruence in \(\mathbb{Z}^ n\) and the dimension of a multidimensional circulant

DOI10.1016/0012-365X(94)00361-LzbMath0827.05029arXiv1209.4984OpenAlexW3098117359MaRDI QIDQ1894764

Yanyan Li

Publication date: 27 November 1995

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.4984

zbMATH Keywords

Cayley graphabelian groupsdimensioncongruenceCayley digraphcirculantintegral matrixmultidimensional circulants

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Directed graphs (digraphs), tournaments (05C20) Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60)

Related Items (12)

Abelian Cayley digraphs with asymptotically large order for any given degree ⋮ On rational matrix exact covering systems of \(\mathbb{Z}^n\) and its applications to Ramanujan's forty identities ⋮ Triple loop networks with small transmission delay ⋮ The Dilating Method for Cayley digraphs on finite Abelian groups ⋮ New Moore-like bounds and some optimal families of abelian Cayley mixed graphs ⋮ On the critical group of the \(n\)-cube ⋮ Parallel optimization and performance tuning on a Kunpeng cluster of genetic algorithm for synthesis of circulant networks ⋮ A geometric approach to dense Cayley digraphs of finite abelian groups ⋮ New dense families of triple loop networks ⋮ Endo-circulant digraphs: Connectivity and generalized cycles ⋮ An improved Moore bound and some new optimal families of mixed abelian Cayley graphs ⋮ Identifying codes of degree 4 Cayley graphs over abelian groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Double commutative-step digraphs with minimum diameters
• Congruences in \({\mathbb{Z}}^ n\), finite Abelian groups and the Chinese remainder theorem
• Isomorphisms of Cayley multigraphs of degree 4 on finite Abelian groups
• Isomorphism of circulant graphs and digraphs
• On a Class of Fixed-Point-Free Graphs
• Circulants and their connectivities
• Circulants and the Characterization of Vertex-Transitive Graphs
• Two theorems on matrices
• Point-symmetric graphs with a prime number of points
• Isomorphism problem for a special class of graphs
• Graphs with circulant adjacency matrices

This page was built for publication: On congruence in \(\mathbb{Z}^ n\) and the dimension of a multidimensional circulant