On the number of  -gons in finite projective planes

doi:10.1285/i15900932v29n1supplp135

On the number of $k$ -gons in finite projective planes

Felix Lazebnik, Keith E. Mellinger, Oscar Vega

Abstract

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

Keywords:
Projective planes; embeddings; k-cycles; Levi graphs

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This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.

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Note di Matematica

On the number of -gons in finite projective planes

Abstract

On the number of $k$ -gons in finite projective planes