An infinite family of integral graphs
type: Item
instance of: scholarly article
title: An infinite family of integral graphs
zbMATH Open document ID: 0556.05049
DOI: 10.1016/0012-365X(84)90095-5
author: Moshe Roitman
published in: Discrete Mathematics
publication date: 1984-01-01T00:00:00Z
review text: The author constructs an infinite family of complete tripartite graphs all of whose eigenvalues are integers. These graphs are denoted \(K(p_ 1,p_ 2,p_ 3)\) with \(p_ 1=4u^ 2(u^ 2+v^ 2)^ 3,\) \(p_ 2=4v^ 2(u^ 2+v^ 2)^ 3,\) \(p_ 3=3u^ 2v^ 2(34u^ 2v^ 2-u^ 4-v^ 4)\) where u and v are positive integers with \((3-\sqrt{8})v<u<v.\) He remarks that other infinite families of integral complete n-partite graphs probably exist with \(n>3\). Indeed, there are probably other infinite families with \(n=3\).
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 3885956
zbMATH Keywords: spectrum
zbMATH Keywords: complete tripartite graphs
zbMATH Keywords: eigenvalues
zbMATH Keywords: integral complete n- partite
MaRDI profile type: Publication
cites work: Q4060995
full work available at URL: 0012-365x(84)90095-5
OpenAlex ID: W2055178321
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description: scientific article; zbMATH DE number 3885956