Spectral characterization of a specific class of trees

TL;DR

This paper demonstrates that a specific class of trees, denoted as T_4(p,q,r), can be uniquely identified by their Laplacian spectrum, and no two non-isomorphic trees in this class share the same adjacency spectrum.

Contribution

It establishes spectral characterization results for the class T_4(p,q,r), showing uniqueness by Laplacian spectrum and spectral distinction by adjacency spectrum.

Findings

T_4(p,q,r) trees are determined by their Laplacian spectrum.

No two non-isomorphic T_4(p,q,r) trees are cospectral with respect to adjacency spectrum.

Spectral properties can distinguish non-isomorphic trees in this class.

Abstract

In this paper, it is shown that the graph $T_4(p,q,r)$ is determined by its Laplacian spectrum and there are no two non-isomorphic such graphs which are cospectral with respect to adjacency spectrum.