Geodesic
Complete graphs with zero diagonal inverse
Ars Mathematica Contemporanea, Tome 11 (2016) no. 2, pp. 231-245.

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If the inverse of a non-singular real symmetric matrix that represents an edge-weighted graph with no loops has zero diagonal, then the inverse itself is the matrix of a loopless graph. Here we show that such graphs having non--zero weight on each edge always exist if their number of vertices is at least 6.
DOI : 10.26493/1855-3974.639.249
Keywords: NSSD, G-nutful graph, circulant matrix, complete graph. 
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Alexander Farrugia; John Baptist Gauci; Irene Sciriha. Complete graphs with zero diagonal inverse. Ars Mathematica Contemporanea, Tome 11 (2016) no. 2, pp. 231-245. doi : 10.26493/1855-3974.639.249. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.639.249/

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