A characterization of all graphs cospectral to the double star $P_2(1,n)$

Fuente: arXiv

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Bibliographische Detailangaben
Hauptverfasser:	Barranca, Emily, Barrus, Michael D.
Format:	Preprint
Veröffentlicht:	2025
Schlagworte:	Combinatorics 05C50
Online-Zugang:	Acceder al recurso
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_version_	1866913884848259072
author	Barranca, Emily Barrus, Michael D.
author_facet	Barranca, Emily Barrus, Michael D.
contents	We examine the adjacency spectrum of trees with diameter three, also referred to as double stars. Using $P_2(a,b)$ to denote a double star with $ a$ and $b$ leaves at its respective endpoints, we discuss graphs which are cospectral to double stars for various parameters $a$ and $b$. In particular, we give constructions for graphs cospectral to $P_2(1,2k)$ for integers $k$. Lastly, we show that the double star $P_2(1,n)$ is determined by its spectrum when $n$ is odd. That is, if a graph $G$ cospectral to $P_2(1,n)$ for odd $n$, then $G$ is isomorphic to $P_2(1,n)$.
format	Preprint
id	arxiv_https___arxiv_org_abs_2506_06934
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	A characterization of all graphs cospectral to the double star $P_2(1,n)$ Barranca, Emily Barrus, Michael D. Combinatorics 05C50 We examine the adjacency spectrum of trees with diameter three, also referred to as double stars. Using $P_2(a,b)$ to denote a double star with $ a$ and $b$ leaves at its respective endpoints, we discuss graphs which are cospectral to double stars for various parameters $a$ and $b$. In particular, we give constructions for graphs cospectral to $P_2(1,2k)$ for integers $k$. Lastly, we show that the double star $P_2(1,n)$ is determined by its spectrum when $n$ is odd. That is, if a graph $G$ cospectral to $P_2(1,n)$ for odd $n$, then $G$ is isomorphic to $P_2(1,n)$.
title	A characterization of all graphs cospectral to the double star $P_2(1,n)$
topic	Combinatorics 05C50
url	https://arxiv.org/abs/2506.06934