The determinant of the distance matrix of graphs with blocks at most bicyclic

DRATMAN, EZEQUIEL; GRIPPO, LUCIANO N.; SAFE, MARTÍN D.; DA SILVA, CELSO M.; DEL-VECCHIO, RENATA R.

LINEAR ALGEBRA AND ITS APPLICATIONS

ELSEVIER SCIENCE INC

Lugar: Amsterdam; Año: 2021 vol. 614 p. 437 - 454

0024-3795

Let G be a connected graph on n vertices and be its distance matrix. The formula for computing the determinant of this matrix in terms of the number of vertices is known when the graph is either a tree or a unicyclic graph. In this work we generalize these results, obtaining the determinant of the distance matrix of any graph whose block decomposition consists of edges, unicyclic and bicyclic graphs.