Tricyclic graphs with the second largest distance eigenvalue less than −12

Kexin Yang; Ligong Wang

doi:10.1016/j.dam.2026.04.039

Tricyclic graphs with the second largest distance eigenvalue less than −12

Kexin Yang
, Ligong Wang

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

Research output: Contribution to journal › Article › peer-review

Abstract

Let G be a simple connected graph with vertex set V(G)={v₁,v₂,…,v_n}. The distance d_G(v_i,v_j) between two vertices v_i and v_j of G is the length of a shortest path between v_i and v_j. The distance matrix of G is the matrix D(G)=(dG(vi,vj))_n×n. The second largest distance eigenvalue of G is the second largest eigenvalue of D(G). Guo and Zhou (2024) proved that any connected graph with the second largest distance eigenvalue less than −12 is chordal, and characterized all bicyclic graphs and split graphs with the second largest distance eigenvalue less than −12. In this paper, we characterize all tricyclic graphs with the second largest distance eigenvalue less than −12.

Original language	English
Pages (from-to)	137-145
Number of pages	9
Journal	Discrete Applied Mathematics
Volume	391
DOIs	https://doi.org/10.1016/j.dam.2026.04.039
State	Published - 15 Oct 2026

Keywords

Chordal graphs
Second largest distance eigenvalue
Tricyclic graphs

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10.1016/j.dam.2026.04.039

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title = "Tricyclic graphs with the second largest distance eigenvalue less than −12",

abstract = "Let G be a simple connected graph with vertex set V(G)=\{v1,v2,…,vn\}. The distance dG(vi,vj) between two vertices vi and vj of G is the length of a shortest path between vi and vj. The distance matrix of G is the matrix D(G)=(dG(vi,vj))n×n. The second largest distance eigenvalue of G is the second largest eigenvalue of D(G). Guo and Zhou (2024) proved that any connected graph with the second largest distance eigenvalue less than −12 is chordal, and characterized all bicyclic graphs and split graphs with the second largest distance eigenvalue less than −12. In this paper, we characterize all tricyclic graphs with the second largest distance eigenvalue less than −12.",

keywords = "Chordal graphs, Second largest distance eigenvalue, Tricyclic graphs",

author = "Kexin Yang and Ligong Wang",

note = "Publisher Copyright: {\textcopyright} 2026 Elsevier B.V.",

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doi = "10.1016/j.dam.2026.04.039",

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T1 - Tricyclic graphs with the second largest distance eigenvalue less than −12

AU - Yang, Kexin

AU - Wang, Ligong

PY - 2026/10/15

Y1 - 2026/10/15

N2 - Let G be a simple connected graph with vertex set V(G)={v1,v2,…,vn}. The distance dG(vi,vj) between two vertices vi and vj of G is the length of a shortest path between vi and vj. The distance matrix of G is the matrix D(G)=(dG(vi,vj))n×n. The second largest distance eigenvalue of G is the second largest eigenvalue of D(G). Guo and Zhou (2024) proved that any connected graph with the second largest distance eigenvalue less than −12 is chordal, and characterized all bicyclic graphs and split graphs with the second largest distance eigenvalue less than −12. In this paper, we characterize all tricyclic graphs with the second largest distance eigenvalue less than −12.

AB - Let G be a simple connected graph with vertex set V(G)={v1,v2,…,vn}. The distance dG(vi,vj) between two vertices vi and vj of G is the length of a shortest path between vi and vj. The distance matrix of G is the matrix D(G)=(dG(vi,vj))n×n. The second largest distance eigenvalue of G is the second largest eigenvalue of D(G). Guo and Zhou (2024) proved that any connected graph with the second largest distance eigenvalue less than −12 is chordal, and characterized all bicyclic graphs and split graphs with the second largest distance eigenvalue less than −12. In this paper, we characterize all tricyclic graphs with the second largest distance eigenvalue less than −12.

KW - Chordal graphs

KW - Second largest distance eigenvalue

KW - Tricyclic graphs

UR - https://www.scopus.com/pages/publications/105038153000

U2 - 10.1016/j.dam.2026.04.039

DO - 10.1016/j.dam.2026.04.039

M3 - 文章

AN - SCOPUS:105038153000

SN - 0166-218X

VL - 391

SP - 137

EP - 145

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Tricyclic graphs with the second largest distance eigenvalue less than −12

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Keywords

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