Infinite generalized friendship graphs
type: Item
instance of: scholarly article
title: Infinite generalized friendship graphs
zbMATH Open document ID: 0539.05053
DOI: 10.1016/0012-365X(84)90162-6
author: Geňa Hahn
author: C. Delorme
published in: Discrete Mathematics
publication date: 1984-01-01T00:00:00Z
review text: Let \(\tau\geq 2\) and \(\lambda\geq 1\) be integers, and let c be an infinite cardinal number. It is shown that \(\tau \leq \lambda +1\) is necessary and sufficient for the existence of (simple) infinite graphs of order c such that every subset of \(\tau\) vertices has exactly \(\lambda\) common neighbors. Furthermore, whe\(n\tau \leq \lambda +1\) then for each c and for each d \((\tau +1\leq d\leq \aleph_ 0)\) there exist \(2^ c\) such pairwise non-isomorphic graphs of order c and chromatic number d. When \(\lambda\geq 2\), any such graph of order c and its complement must both be regular of degree c.
Mathematics Subject Classification ID: 05C99
zbMATH DE Number: 3857164
zbMATH Keywords: infinite graphs
zbMATH Keywords: friendship graphs
MaRDI profile type: Publication
cites work: Q5422499
cites work: Q5617643
cites work: Graphs in which each m-tuple of vertices is adjacent to the same number n of other vertices
cites work: There are 2ℵα Friendship Graphs of Cardinal ℵα
cites work: Q4079638
cites work: Graph Theory and Probability
cites work: Q5520566
cites work: On chromatic number of graphs and set-systems
cites work: Q3257866
cites work: Paths and Circuits in Critical Graphs
cites work: Degrees of Vertices in a Friendship Graph
cites work: Q5654053
cites work: Q3890733
cites work: Q4068763
cites work: A Variation of the Friendship Theorem
cites work: Q4141847
cites work: Q5632577
full work available at URL: 0012-365x(84)90162-6
OpenAlex ID: W1968986139
description: scientific article; zbMATH DE number 3857164