Work

On graphs whose third Laplacian matching root is small

Year: 2025

Type: article

Abstract: Let $$\gamma _2(G)$$ γ 2 ( G ) and $$\gamma _3(G)$$ γ 3 ( G ) be the second and the third largest roots of the Laplacian matching polynomial of a simple graph G . In this note we structurally characterize the graphs in the sets $$\mathcal {S}' \subset \mathcal {S}$$ S ′ ⊂ S , where $$\mathcal {S}= \{ G \mid \gamma _3(G) <2 \}$$ S = { G ∣ γ 3 ( G ) < 2 } and $$\mathcal {S}'= \{ G \mid \gamma _2(G) \geqslant 2, \; \gamma _3(G) <2 \}$$ S ′ = { G ∣ γ 2 ( G ) ⩾ 2 , γ 3 ( G ) < 2 } .

Source: Ricerche di Matematica

DOI: 10.1007/s11587-025-01040-1

Authors: Mengge Li, Maurizio Brunetti, Jianfeng Wang

Institutions: Shandong University of Technology, University of Naples Federico II

Language: English

Topic: Graph theory and applications

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190