Geodesic
No chemical graph on more than two vertices is nuciferous
Ars Mathematica Contemporanea, Tome 11 (2016) no. 2, pp. 397-402.

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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 K2, 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.
DOI : 10.26493/1855-3974.1030.9d9
Keywords: Nuficerous graph, chemical graph, NSSD, non-singular graph, molecular conductivity 
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Irene Sciriha; Alexander Farrugia. No chemical graph on more than two vertices is nuciferous. Ars Mathematica Contemporanea, Tome 11 (2016) no. 2, pp. 397-402. doi : 10.26493/1855-3974.1030.9d9. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1030.9d9/

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