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2012 | 32 | 1 | 153-160
Tytuł artykułu

On a generalization of the friendship theorem

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The Friendship Theorem states that if any two people, of a group of at least three people, have exactly one friend in common, then there is always a person who is everybody's friend. In this paper, we generalize the Friendship Theorem to the case that in a group of at least three people, if every two friends have one or two common friends and every pair of strangers have exactly one friend then there exist one person who is friend to everybody in the group. In particular, we show that the graph corresponding to this problem is of type G = K₁∨(sK₂ + tK₃), where s and t are non-negative integers and Kₘ is the complete graph on m vertices.
Słowa kluczowe
Wydawca
Rocznik
Tom
32
Numer
1
Strony
153-160
Opis fizyczny
Daty
wydano
2012
otrzymano
2010-05-21
poprawiono
2011-04-01
zaakceptowano
2011-04-01
Twórcy
  • Department of Mathematical Sciences, University of South Carolina Aiken, Aiken, SC 29801
Bibliografia
  • [1] J. Bondy, Kotzig's Conjecture on generalized friendship graphs - a survey, Annals of Discrete Mathematics 27 (1985) 351-366.
  • [2] P. Erdös, A. Rènyi and V. Sós, On a problem of graph theory, Studia Sci. Math 1 (1966) 215-235.
  • [3] R. Gera and J. Shen, Extensions of strongly regular graphs, Electronic J. Combin. 15 (2008) # N3 1-5.
  • [4] J. Hammersley, The friendship theorem and the love problem, in: Surveys in Combinatorics, London Math. Soc., Lecture Notes 82 (Cambridge University Press, Cambridge, 1989) 127-140.
  • [5] N. Limaye, D. Sarvate, P. Stanika and P. Young, Regular and strongly regular planar graphs, J. Combin. Math. Combin. Compt 54 (2005) 111-127.
  • [6] J. Longyear and T. Parsons, The friendship theorem, Indag. Math. 34 (1972) 257-262.
  • [7] E. van Dam and W. Haemers, Graphs with constant μ and μ̅, Discrete Math. 182 (1998) 293-307, doi: 10.1016/S0012-365X(97)00150-7.
  • [8] H. Wilf, The friendship theorem in combinatorial mathematics and its applications, Proc. Conf. Oxford, 1969 (Academic Press: London and New York, 1971) 307-309.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1593
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