Distance Matrix of a Multi-block Graph: Determinant and Inverse

TL;DR

This paper computes the determinant and inverse of the distance matrix for multi-block graphs, a class of graphs composed of complete multi-partite blocks, extending previous work on related graph classes.

Contribution

It provides explicit formulas for the determinant and inverse of the distance matrix for multi-block graphs, advancing understanding of their structural properties.

Findings

Derived formulas for the determinant of the distance matrix.

Explicit inverse of the distance matrix for multi-block graphs.

Extended previous results to a broader class of graphs.

Abstract

A connected graph is called a multi-block graph if each of its blocks is a complete multi-partite graph. Building on the work of \cite{Bp3,Hou3}, we compute the determinant and inverse of the distance matrix for a class of multi-block graphs.