The centipede is determined by its Laplacian spectrum

TL;DR

This paper proves that the Laplacian spectrum uniquely identifies centipede graphs, which are formed by attaching pendant vertices to a path, thus solving a spectral characterization problem.

Contribution

It establishes that centipede graphs are uniquely determined by their Laplacian spectra, a previously unresolved spectral characterization issue.

Findings

Centipede graphs are uniquely identified by their Laplacian spectra.

The proof confirms the spectral determination of this class of graphs.

This advances understanding of spectral graph theory and graph identification.

Abstract

A centipede is a graph obtained by appending a pendant vertex to each vertex of degree 2 of a path. In this paper we prove that the centipede is determined by its Laplacian spectrum.