A note on constructing large Cayley graphs of given degree and diameter by voltage assignments
type: Item
instance of: scholarly article
title: A note on constructing large Cayley graphs of given degree and diameter by voltage assignments
zbMATH Open document ID: 0885.05071
author: Mirka Miller
author: Ján Plesník
author: Jozef Širáň
author: Ljiljana Brankovic
author: Joe Ryan
published in: The Electronic Journal of Combinatorics
publication date: 1998-02-18T00:00:00Z
full work available at URL: v5i1r9.html
review text: Summary: Voltage graphs are a powerful tool for constructing large graphs (called lifts) with prescribed properties as covering spaces of small base graphs. This makes them suitable for application to the degree/diameter problem, which is to determine the largest order of a graph with given degree and diameter. Many currently known largest graphs of degree at most 15 and diameter at most 10 have been found by computer search among Cayley graphs of semidirect products of cyclic groups. We show that all of them can in fact be described as lifts of smaller Cayley graphs of cyclic groups, with voltages in (other) cyclic groups. This opens up a new possible direction in the search for large vertex-transitive graphs of given degree and diameter.
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 1119074
zbMATH Keywords: base graphs
zbMATH Keywords: diameter problem
zbMATH Keywords: Cayley graphs
zbMATH Keywords: cyclic groups
zbMATH Keywords: voltages
zbMATH Keywords: vertex-transitive graphs
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1119074