On the non-existence of Abelian Moore Cayley graphs with excess one

DOI10.47443/dml.2021.0057OpenAlexW4242209040MaRDI QIDQ5051445

Wei He

Publication date: 23 November 2022

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

Full work available at URL: https://doi.org/10.47443/dml.2021.0057

zbMATH Keywords

symmetric functionsgroup ringMoore bounddegree-diameter problemabelian Cayley graph

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Symmetric functions and generalizations (05E05) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Uses Software

• Magma

Cites Work

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• The degree-diameter problem for circulant graphs of degree 8 and 9
• Cayley graphs of given degree and diameter for cyclic, Abelian, and metacyclic groups
• The degree-diameter problem for circulant graphs of degrees 10 and 11
• Regular graphs with excess one
• The Magma algebra system. I: The user language
• Finite geometry and character theory
• No lattice tiling of \(\mathbb{Z}^n\) by Lee sphere of radius 2
• Nonexistence of perfect 2-error-correcting Lee codes in certain dimensions
• On the nonexistence of lattice tilings of \(\mathbb{Z}^n\) by Lee spheres
• On Moore Graphs with Diameters 2 and 3
• Large circulant graphs of fixed diameter and arbitrary degree
• The Degree-Diameter Problem for Several Varieties of Cayley Graphs I: The Abelian Case
• Cayley Graphs of Diameter Two from Difference Sets

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