Unique path property digraphs
Central groupoids, central digraphs, and zero-one matrices A satisfying A2 = J
Journal of Combinatorial Theory Series A
PRESENT: An Ultra-Lightweight Block Cipher
CHES '07 Proceedings of the 9th international workshop on Cryptographic Hardware and Embedded Systems
On Moore graphs with diameters 2 and 3
IBM Journal of Research and Development
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A directed graph is called central if its adjacency matrix A satisfies the equation A^2=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.