Nontrivial nuciferous graphs exist - Ghorbani, Ebrahim (Ars mathematica contemporanea, 2016)
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 ?$K_2$?, no nuciferous graph exists. We disprove this conjecture. Moreover, we conjecture that there are infinitely many nuciferous Cayley graphs.
Keywords: Cayley graph; Cayleyjevi grafi; nuciferični grafi; nuciferous graph