# On a generalization of the friendship theorem

Discussiones Mathematicae Graph Theory (2012)

- Volume: 32, Issue: 1, page 153-160
- ISSN: 2083-5892

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topMohammad Hailat. "On a generalization of the friendship theorem." Discussiones Mathematicae Graph Theory 32.1 (2012): 153-160. <http://eudml.org/doc/271073>.

@article{MohammadHailat2012,

abstract = {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.},

author = {Mohammad Hailat},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {(λ,μ)-graph; Friendship Theorem; -graph; friendship theorem},

language = {eng},

number = {1},

pages = {153-160},

title = {On a generalization of the friendship theorem},

url = {http://eudml.org/doc/271073},

volume = {32},

year = {2012},

}

TY - JOUR

AU - Mohammad Hailat

TI - On a generalization of the friendship theorem

JO - Discussiones Mathematicae Graph Theory

PY - 2012

VL - 32

IS - 1

SP - 153

EP - 160

AB - 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.

LA - eng

KW - (λ,μ)-graph; Friendship Theorem; -graph; friendship theorem

UR - http://eudml.org/doc/271073

ER -

## References

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- [6] J. Longyear and T. Parsons, The friendship theorem, Indag. Math. 34 (1972) 257-262. Zbl0243.05006
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- [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.

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