# A Characterization of Distance Matrices of Positive Weighted Kneser Graphs and Generalized Petersen Graphs

## TL;DR

This paper extends the characterization of distance matrices from positive weighted Petersen graphs to Kneser and generalized Petersen graphs, analyzing their properties and the influence of girth on these matrices.

## Contribution

It generalizes existing results on distance matrices from Petersen graphs to Kneser and generalized Petersen graphs, incorporating girth considerations.

## Key findings

- Generalized properties of distance matrices for Kneser and generalized Petersen graphs.
- Established theorems relating girth to distance matrix properties.
- Extended previous results to a broader class of graphs.

## Abstract

Rubei et. al., established results for the distance matrix of positive weighted Petersen graphs. Focusing on the properties of the distance matrix, we generalized positive weighted Petersen graphs results to Kneser graphs. We analyzed theorems established by Rubei et al. and used girth of the generalized Petersen graphs and Kneser graphs to conclude generalizations. Further, we examined the properties of positive weighted generalized Petersen graphs. We generalized the properties of distance matrices of positive weighted Petersen graphs to positive weighted generalized Petersen graphs.