The rank of the walk matrix of the extended Dynkin graph $\tilde{D}_n$

TL;DR

This paper derives an explicit formula for the rank of the walk matrix associated with the extended Dynkin graph D_n, contributing to spectral graph theory and algebraic combinatorics.

Contribution

It provides a novel explicit formula for the walk matrix rank of D_n, advancing understanding of spectral properties of extended Dynkin graphs.

Findings

Explicit formula for walk matrix rank of D_n

Enhanced understanding of spectral properties of extended Dynkin graphs

Potential applications in algebraic combinatorics and graph theory

Abstract

In this paper, we provide an explicit formula for the rank of the walk matrix of the extended Dynkin graph $\tilde{D}_n$.