Hidden Cayley graph structures
type: Item
instance of: scholarly article
title: Hidden Cayley graph structures
zbMATH Open document ID: 0890.05031
DOI: 10.1016/S0012-365X(97)00134-9
author: Oriol Serra
author: Italo J. Dejter
author: Héctor Hevia
published in: Discrete Mathematics
publication date: 1998-06-22T00:00:00Z
review text: Let \(C\) be a cyclic group of odd order \(n\). A totally multicolored triple of \(C\) is a set of three distinct elemets \(a\), \(b\) and \(c\) of \(C\) such that \(a + b = \pm c\). It is shown that the Cayley graph of \(C\) with respect to a totally multicolored triple with \(\text{gcd}(a,b,c,n) = 1\) is a triangulation of a torus. If two totally multicolored triples share two elements, then the corresponding torus embeddings are related by first deleting one orbit of edges, forming a quadrilateral torus embedding, and then adding another orbit of edges comprising the other diagonals of the quadrilaterals. The authors define a graph \(G_n'\) on the set of totally multicolored triples by setting two triples adjacent if they share two elements and show that the diameter of \(G_n'\) is asymptotic to the square root of \(n\).
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 1121486
zbMATH Keywords: Cayley graph
zbMATH Keywords: graph embedding
zbMATH Keywords: torus embedding
reviewed by: Brigitte Servatius
MaRDI profile type: Publication
cites work: Q3487365
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full work available at URL: s0012-365x(97)00134-9
OpenAlex ID: W2011274282
description: scientific article; zbMATH DE number 1121486