The number of cyclic configurations of type (v₃) and the isomorphism\n problem

2013/01/11 by Sergio Hiroki Koike-Quintanar, István Kovács, Koike-Quintanar, Sergio Hiroki +4 · 1 citation
Computer Science · Engineering · Mathematics · #05C25 #05C60 #20B25 #51E30 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1301.2445

openalex publication_date 2013/01/11 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

A configuration of points and lines is cyclic if it has an automorphism which\npermutes its points in a full cycle. A closed formula is derived for the number\nof non-isomorphic connected cyclic configurations of type (v₃), i.e., which\nhave v points and lines, and each point/line is incident with exactly 3\nlines/points. In addition, a Bays-Lambossy type theorem is proved for cyclic\nconfigurations if the number of points is a product of two primes or a prime\npower.\n

Citations

• Equivalence of sparse circulants: the bipartite Ádám problem

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