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Degrees of Vertices in a Friendship Graph

Published online by Cambridge University Press:  20 November 2018

Anton Kotzig
Anton Kotzig*
Affiliation:
Centre de Recherches Mathématiques, Université de Montréal, Québec, Canada
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Abstract

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A friendship graph is a graph in which every two distinct vertices have exactly one common adjacent vertex (called a neighbour). Finite friendship graphs have been characterized by Erdós, Rényi and Sós [2]: Each finite friendship graph Fn which consists of n edge disjoint triangles such that all n>1 triangles have one vertex in common (F1 is a triangle i.e. the complete graph with three vertices). Thus Fn has 2n+1 vertices, 2n of them being of degree two and the remaining one (the common vertex of n triangles if n>1) being of degree 2n.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 5 , 01 December 1975 , pp. 691 - 693
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Chvátal, V., Kotzig, A., Rosenberg, I. G. and Davies, Roy O., There are K friendship graphs of cardinal (submitted to Canadian Mathematical Bulletin, September 1974).Google Scholar
2. Erdös, P., Rényi, A. and Sös, V. T., On a problem of graph theory, Studia Math. Hungar. 1 (1966), 215–235.Google Scholar
3. Harary, F., Graph theory, Addison-Wesley, Reading, 1969.Google Scholar