Complete graphs with zero diagonal inverse

Alexander Farrugia, John Baptist Gauci, Irene Sciriha

Abstract


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


NSSD, G-nutful graph, circulant matrix, complete graph.

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DOI: https://doi.org/10.26493/1855-3974.639.249

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications