2021/05/19 by Besnard, Fabien · 1 citation
#05C99 #58B34 #Combinatorics (math.CO) #FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2105.09056
We report on some findings concerning Connes' noncommutative distance d on a weighted undirected graph G. Our main result is the lower bound ℓ/Δ(G)≤ d where ℓ is the geodesic distance and Δ(G) the degree of G. It is obtained thanks to an auxiliary spectral triple on the collection of the edges of G.