Nontrivial nuciferous graphs exist

Ebrahim Ghorbani

Abstract


A nuciferous graph is a simple graph with a non-singular 0-1 adjacency matrix A such that all the diagonal entries of A − 1 are zero and all the off-diagonal entries of A − 1 are non-zero. Sciriha et al. conjectured that except K2, no nuciferous graph exists. We disprove this conjecture. Moreover, we conjecture that there are infinitely many nuciferous Cayley graphs.


Keywords


Nuciferous graph, Cayley graph

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DOI: https://doi.org/10.26493/1855-3974.1025.466

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications