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There are 2ℵα Friendship Graphs of Cardinal ℵα

Published online by Cambridge University Press:  20 November 2018

Václav Chvátal ,
Anton Kotzig ,
Ivo G. Rosenberg  and
Roy O. Davies
Václav Chvátal
Affiliation:
Centre De Recherches Mathématiques, Université De Montréal
Anton Kotzig
Affiliation:
Centre De Recherches Mathématiques, Université De Montréal
Ivo G. Rosenberg
Affiliation:
Départment of Mathematics, Leicester University
Roy O. Davies
Affiliation:
Départment of Mathematics, Leicester University
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A friendship graph is a graph in which every two distinct vertices have exactly one common neighbour. Finite friendship graphs were characterized by Erdös, Rényi, and Sós [1] as those for which the vertices can be enumerated as u, υ1,…υk, w1,…wk in such a way that the only edges are uυiuwi and υiwi (i = 1,…,k). Thus finite friendship graphs are rather rare. In contrast, we shall show that there are as many nonisomorphic friendship graphs of given infinite cardinal as there are nonisomorphic graphs of that cardinal altogether. In fact, we do a little more.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 4 , 01 December 1976 , pp. 431 - 433
Copyright
Copyright © Canadian Mathematical Society 1976

References

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