Triple loop networks with small transmission delay
type: Item
instance of: scholarly article
title: Triple loop networks with small transmission delay
zbMATH Open document ID: 0872.05035
DOI: 10.1016/S0012-365X(96)00213-0
author: O. Diekmann
published in: Discrete Mathematics
publication date: 1997-10-05T00:00:00Z
review text: The paper studies the triple loop case of the problem of finding multiloop networks with a fixed number of vertices and small diameter. Based on lattice theory and integral circulant matrices, a method is developed to deal with this problem by constructing three infinite families of triple loop networks with large order for the values of the diameter \(D=2, 4, 5\pmod 6\), showing that \(N(3,D)\geq 2D^3/27+ O(D^2)\), where \(N(3,D)\) is the number of vertices for a triple loop network with diameter \(D\). Similar results are also obtained in the more general frame of triple commutative-step digraphs.
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05C12
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 05B45
Mathematics Subject Classification ID: 05C35
Mathematics Subject Classification ID: 94C15
Mathematics Subject Classification ID: 94C05
zbMATH DE Number: 1018499
zbMATH Keywords: multiloop networks
zbMATH Keywords: diameter
reviewed by: Wai-Kai Chen
MaRDI profile type: Publication
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Wikidata QID: Q127011617
description: scientific article; zbMATH DE number 1018499