✦ LIBER ✦

Minimal harmoniously colorable designs

✍ Scribed by L. R. A. Casse; Christine M. O'Keefe; B. J. Wilson

Book ID: 102310050
Publisher: John Wiley and Sons
Year: 1994
Tongue: English
Weight: 460 KB
Volume: 2
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.3180020203

No coin nor oath required. For personal study only.

✦ Synopsis

A graph G is minimal harmoniously colorable if it has a proper vertex coloring in which each pair of colors occurs exactly once on a n edge. In particular, if D is a 2-design we consider the graph G whose vertices are the points and blocks of D and where two vertices of G are adjacent if and only if the corresponding elements of D are incident. It will be shown that if D is symmetric then G is minimal harmoniously colorable if and only if D is a Hadamard design with corresponding Hadamard matrix of a certain form. We obtain some results if D is nonsymmetric, and construct two classes of nonsymmetric minimal harmoniously colorable designs.

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