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On The Number Of K-Gons In Finite Projective Planes, Felix Lazebnik, Keith Mellinger, Oscar Vega
On The Number Of K-Gons In Finite Projective Planes, Felix Lazebnik, Keith Mellinger, Oscar Vega
Mathematics
Let π = πq denote a finite projective plane of order q, and let G = Levi(π) be the bipartite point-line incidence graph of π. For k ≥ 3, let c2k(π) denote the number of cycles of length 2k in G. Are the numbers c2k(π) the same for all πq? We prove that this is the case for k = 3, 4, 5, 6 by computing these numbers.