Super-Simple Twofold Steiner Pentagon Systems

Autor: F. E. Bennett, R. J. R. Abel
Rok vydání: 2011
Předmět:
Zdroj: Graphs and Combinatorics. 28:297-308
ISSN: 1435-5914
0911-0119
DOI: 10.1007/s00373-011-1053-y
Popis: A twofold pentagon system of order v is a decomposition of the complete undirected 2-multigraph 2K v into pentagons. A twofold Steiner pentagon system of order v [TSPS(v)] is a twofold pentagon system such that every pair of distinct vertices is joined by a path of length two in exactly two pentagons of the system. A TSPS(v) is said to be super-simple if its underlying (v, 5, 4)-BIBD is super-simple; that is, if any two blocks of the BIBD intersect in at most two points. In this paper, it is shown that the necessary conditions for the existence of a super-simple TSPS(v); namely, v ≥ 15 and v ≡ 0 or 1 (mod 5) are sufficient. For these specified orders, the main result of this paper also guarantees the existence of a very special and interesting class of twofold and fourfold Steiner pentagon systems of order v with the additional property that, for any two vertices, the two or four paths of length two joining them are distinct.
Databáze: OpenAIRE
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