Inverse Formulae for $q$-analogues of Bipartite Distance Matrix

TL;DR

This paper derives inverse formulae for two $q$-analogues of bipartite distance matrices, extending previous results and introducing a $q$-analogue bipartite Laplacian matrix.

Contribution

It provides explicit inverse formulae for the $q$-bipartite distance and exponential distance matrices, and introduces a $q$-analogue bipartite Laplacian matrix.

Findings

Explicit inverse formulae for $q$-bipartite distance matrices

Extension of existing bipartite distance matrix results

Introduction of a $q$-analogue bipartite Laplacian matrix

Abstract

We consider two distinct $q$-analogues of the bipartite distance matrix, namely the $q$-bipartite distance matrix and the exponential distance matrix. We provide formulae of the inverse for these matrices, which extend the existing results for the bipartite distance matrix. These investigations lead us to introduce a $q$-analogue version of the bipartite Laplacian matrix.