Complete graphs with zero diagonal inverse - Farrugia, Alexander (Ars mathematica contemporanea, 2016)
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.
Keywords: circulant matrix; cirkulantna matrika; complete graph; G-matični graf; G-nutful graph; NSSD; polni graf