Mertzios, G.B. and Unger, W. (2016) 'The friendship problem on graphs.', Journal of multiple-valued logic and soft computing., 27 (2-3). pp. 275-285.
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.
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||http://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-27-number-2-3-2016/mvlsc-27-2-3-p-275-285/|
|Date accepted:||03 October 2014|
|Date deposited:||02 September 2016|
|Date of first online publication:||01 August 2016|
|Date first made open access:||01 July 2017|
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