The determinant of the distance matrix of graphs with at most two cycles

2019/12/20 by Dratman, Ezequiel, Grippo, Luciano N., Safe, Matín D. +2
#Combinatorics (math.CO) #FOS: Mathematics #G.2.1

paper · doi:10.48550/arxiv.1912.09604

Abstract

Let G be a connected graph on n vertices and D(G) 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 for all graphs in a class, including trees, unicyclic and bicyclic graphs. This class actually includes graphs with many cycles, provided that each block of the graph is at most bicyclic.

Related

• On the determinant of the distance matrix of a bicyclic graph
• Distance Matrix of a Multi-block Graph: Determinant and Inverse
• On distance matrices of graphs
• On the distance matrices of the CP graphs
• Distance Matrix of Weighted Cactoid-type Digraphs