Journal article
Switchings, extensions, and reductions in central digraphs
A directed graph is called central if its adjacency matrix A satisfies the equation A2=J, where J is the matrix with a 1 in each entry. It has been conjectured that every central directed graph can be obtained from a standard example by a sequence of simple operations called switchings, and also that it can be obtained from a smaller one by an extension.
We disprove these conjectures and present a general extension result which, in particular, shows that each counterexample extends to an infinite family.
Language: | English |
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Year: | 2011 |
Pages: | 2025-2034 |
ISSN: | 10960899 and 00973165 |
Types: | Journal article |
DOI: | 10.1016/j.jcta.2011.03.009 |
ORCIDs: | Thomassen, Carsten |