Geodesic
Degrees of Vertices in a Friendship Graph
Canadian mathematical bulletin, Tome 18 (1975) no. 5, pp. 691-693

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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. 
Kotzig, Anton. Degrees of Vertices in a Friendship Graph. Canadian mathematical bulletin, Tome 18 (1975) no. 5, pp. 691-693. doi: 10.4153/CMB-1975-120-x
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     title = {Degrees of {Vertices} in a {Friendship} {Graph}},
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