Geodesic
On Point-Symmetric Tournaments
Canadian mathematical bulletin, Tome 13 (1970) no. 3, pp. 317-323

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A tournament is a directed graph in which there is exactly one arc between any two distinct vertices. Let denote the automorphism group of T. A tournament T is said to be point-symmetric if acts transitively on the vertices of T. Let g(n) be the maximum value of taken over all tournaments of order n. In [3] Goldberg and Moon conjectured that with equality holding if and only if n is a power of 3. The case of point-symmetric tournaments is what prevented them from proving their conjecture. In [2] the conjecture was proved through the use of a lengthy combinatorial argument involving the structure of point-symmetric tournaments. The results in this paper are an outgrowth of an attempt to characterize point-symmetric tournaments so as to simplify the proof employed in [2]. 
Alspach, Brian. On Point-Symmetric Tournaments. Canadian mathematical bulletin, Tome 13 (1970) no. 3, pp. 317-323. doi: 10.4153/CMB-1970-061-7
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     title = {On {Point-Symmetric} {Tournaments}},
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     year = {1970},
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     doi = {10.4153/CMB-1970-061-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-061-7/}
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