No chemical graph on more than two vertices is nuciferous - Sciriha, Irene (Ars mathematica contemporanea, 2016)
A simple graph is nuciferous if its ?$0-1$? adjacency matrix is nonsingular and if its inverse has zero entries on its main diagonal and a non-zero entry at each off-diagonal position. A nuciferous graph is a molecular graph that represents an ipso omni-insulating but distinct omni-conducting molecule. It has been conjectured in 2012 that only ?$K_2$?, the complete graph on two vertices, is nuciferous. We show that this conjecture is true for chemical graphs, that is, graphs whose vertex degree is at most three.
Keywords: chemical graph; kemični grafi; molecular conductivity; molekularna konduktivnost; nesingularni grafi; non-singular graph; NSSD; nuciferični grafi; nuciferous graph