On a generalization of the friendship theorem

• Autorzy: Mohammad Hailat
• 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

EN

(λ,μ)-graph; Friendship Theorem

Kategorie tematyczne

• 05C75: Structural characterization of families of graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2012
• Tom: 32
• Numer: 1
• Strony: 153-160

Daty

wydano

2012

otrzymano

2010-05-21

poprawiono

2011-04-01

zaakceptowano

2011-04-01

Twórcy

autor

Mohammad Hailat

• Department of Mathematical Sciences, University of South Carolina Aiken, Aiken, SC 29801

Bibliografia

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• [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.

Identyfikatory

DOI

10.7151/dmgt.1593