Geodesic
Nontrivial nuciferous graphs exist
Ars Mathematica Contemporanea, Tome 11 (2016) no. 2, pp. 391-395.

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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.
DOI : 10.26493/1855-3974.1025.466
Keywords: Nuciferous graph, Cayley graph 
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Ebrahim Ghorbani. Nontrivial nuciferous graphs exist. Ars Mathematica Contemporanea, Tome 11 (2016) no. 2, pp. 391-395. doi : 10.26493/1855-3974.1025.466. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1025.466/

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