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Minimal harmoniously colorable designs
Author(s) -
Casse L. R. A.,
O'Keefe Christine M.,
Wilson B. J.
Publication year - 1994
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.3180020203
Subject(s) - combinatorics , mathematics , hadamard transform , vertex (graph theory) , graph , hadamard matrix , discrete mathematics , mathematical analysis
A graph G is minimal harmoniously colorable if it has a proper vertex coloring in which each pair of colors occurs exactly once on an 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. © 1994 John Wiley & Sons, Inc.