The Hoffman program for mixed graphs

Yuantian Yu; Edwin R. van Dam

doi:10.1016/j.laa.2025.07.034

The Hoffman program for mixed graphs

Yuantian Yu
, Edwin R. van Dam^*

^*Corresponding author for this work

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Abstract

We consider Hoffman's program about the limit points of the spectral radius of the Hermitian adjacency matrix of mixed graphs. In particular, we determine all such limit points. As an intermediate step, we determine all mixed graphs without negative 4-cycle whose spectral radius does not exceed root2+root5.

Original language	English
Pages (from-to)	436-457
Number of pages	22
Journal	Linear Algebra and its Applications
Volume	726
DOIs	https://doi.org/10.1016/j.laa.2025.07.034
Publication status	Published - Dec 2025

Keywords

limit points
Mixed graph
Spectral radius
root 2+root 5

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10.1016/j.laa.2025.07.034Licence: CC BY

The Hoffman program for mixed graphsFinal published version, 1.01 MBLicence: CC BY

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title = "The Hoffman program for mixed graphs",

abstract = "We consider Hoffman's program about the limit points of the spectral radius of the Hermitian adjacency matrix of mixed graphs. In particular, we determine all such limit points. As an intermediate step, we determine all mixed graphs without negative 4-cycle whose spectral radius does not exceed root2+root5.",

keywords = "limit points, Mixed graph, Spectral radius, root 2+root 5",

author = "Yuantian Yu and \{van Dam\}, \{Edwin R.\}",

year = "2025",

month = dec,

doi = "10.1016/j.laa.2025.07.034",

language = "English",

volume = "726",

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AU - Yu, Yuantian

AU - van Dam, Edwin R.

PY - 2025/12

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N2 - We consider Hoffman's program about the limit points of the spectral radius of the Hermitian adjacency matrix of mixed graphs. In particular, we determine all such limit points. As an intermediate step, we determine all mixed graphs without negative 4-cycle whose spectral radius does not exceed root2+root5.

AB - We consider Hoffman's program about the limit points of the spectral radius of the Hermitian adjacency matrix of mixed graphs. In particular, we determine all such limit points. As an intermediate step, we determine all mixed graphs without negative 4-cycle whose spectral radius does not exceed root2+root5.

KW - limit points

KW - Mixed graph

KW - Spectral radius

KW - root 2+root 5

UR - https://www.mendeley.com/catalogue/8aadc9cd-2380-3b00-acdf-ed8f262cddbb/

U2 - 10.1016/j.laa.2025.07.034

DO - 10.1016/j.laa.2025.07.034

M3 - Article

SN - 0024-3795

VL - 726

SP - 436

EP - 457

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -

The Hoffman program for mixed graphs

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Keywords

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