Switchings, extensions, and reductions in central digraphs

Publication: Research - peer-reviewJournal article – Annual report year: 2011

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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.
Original languageEnglish
JournalJournal of Combinatorial Theory, Series A
Publication date2011
Volume118
Issue7
Pages2025-2034
ISSN0097-3165
DOIs
StatePublished
CitationsWeb of Science® Times Cited: 1

Keywords

  • Unique path property, Central directed graph, Central groupoid
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