Dr George Mertzios george.mertzios@durham.ac.uk
Associate Professor
The friendship problem on graphs
Mertzios, G.B.; Unger, W.
Authors
W. Unger
Abstract
In this paper we provide a purely combinatorial proof of the Friendship Theorem, which has been first proven by P. Erdős et al. by using also algebraic methods. Moreover, we generalize this theorem in a natural way, assuming that every pair of nodes occupies l ≥ 2 common neighbors. We prove that every graph, which satisfies this generalized l-friendship condition, is a regular graph.
Citation
Mertzios, G., & Unger, W. (2016). The friendship problem on graphs. Journal of Multiple-Valued Logic and Soft Computing, 27(2-3), 275-285
Journal Article Type | Article |
---|---|
Acceptance Date | Oct 3, 2014 |
Online Publication Date | Aug 1, 2016 |
Publication Date | Aug 1, 2016 |
Deposit Date | Sep 1, 2016 |
Publicly Available Date | Jul 1, 2017 |
Journal | Journal of Multiple-Valued Logic and Soft Computing |
Print ISSN | 1542-3980 |
Electronic ISSN | 1542-3999 |
Publisher | Old City Publishing |
Peer Reviewed | Peer Reviewed |
Volume | 27 |
Issue | 2-3 |
Pages | 275-285 |
Publisher URL | http://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-27-number-2-3-2016/mvlsc-27-2-3-p-275-285/ |
Files
Accepted Journal Article
(79 Kb)
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