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math.CO2023
The additive-multiplicative distance matrix of a graph, and a novel third invariant
Projesh Nath Choudhury, Apoorva Khare
Graham showed with Pollak and Hoffman-Hosoya that for any directed graph with strong blocks , the determinant and cofactor-sum of the distance matri…
math.RA2023
Sign regular matrices and variation diminution: single-vector tests and characterizations, following Schoenberg, Gantmacher-Krein, and Motzkin
Projesh Nath Choudhury, Shivangi Yadav
Variation diminution (VD) is a fundamental property in total positivity theory, first studied in 1912 by Fekete-Pólya for one-sided Pólya frequency sequences, followed by Schoenber…
math.CO2023
Quadratic embedding constants of graphs: Bounds and distance spectra
Projesh Nath Choudhury, Raju Nandi
The quadratic embedding constant (QEC) of a finite, simple, connected graph is the maximum of the quadratic form of the distance matrix of on the subset of the unit sphere…