On the number of k-gons in finite projective planes


Let \pi = \pi _q denote a finite projective plane of order q,  and let G = Levi (\pi) be the bipartite point-line incidence graph of  \pi.  For k\ge 3,  let c_{2k} (\pi) denote the number of  cycles of length 2k in G.   Are the numbers c_{2k} (\pi) the same for all \pi _q?  We prove that this is the case for k=3,4,5,6 by computing these numbers.

DOI Code: 10.1285/i15900932v29n1supplp135

Projective planes; embeddings; k-cycles; Levi graphs

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