Graphs whose spectral radius is bounded by a fixed Hoffman–Smith limit point

For an integer p ≥ 3 , we study graphs whose adjacency spectral radius satisfies ρ ( G ) < p p - 1 = A p or whose signless Laplacian spectral radius satisfies κ ( G ) < p 2 p - 1 = Q p . The numbers A p and Q p are known as Hoffman–Smith limit points. For general p , we find upper bounds on th...

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Veröffentlicht in:Journal of algebraic combinatorics Jg. 62; H. 2; S. 25
Hauptverfasser: Borba, Elizandro Max, Calegari, Rafael, Hoppen, Carlos, Trevisan, Vilmar, Veloso, Bruno Scaratti
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.09.2025
Springer Nature B.V
Schlagworte:
Combinatorics
Computer Science
Convex and Discrete Geometry
Eigenvalues
Graphs
Group Theory and Generalizations
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
Upper bounds
Hoffman–Smith limit points
Hoffman program
Graph subdivision
ISSN:0925-9899, 1572-9192
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Zusammenfassung:For an integer p ≥ 3 , we study graphs whose adjacency spectral radius satisfies ρ ( G ) < p p - 1 = A p or whose signless Laplacian spectral radius satisfies κ ( G ) < p 2 p - 1 = Q p . The numbers A p and Q p are known as Hoffman–Smith limit points. For general p , we find upper bounds on the maximum degree of such graphs G and describe the graphs for which the upper bound is achieved with respect to the adjacency matrix. Moreover, we describe forbidden substructures for graphs in these classes. For p = 4 , we show that the structure of graphs G such that A 3 < ρ ( G ) < A 4 or Q 3 < κ ( G ) < Q 4 is much richer than the structure of graphs for which ρ ( G ) < A 3 or κ ( G ) < Q 3 , whose study has been initiated by Woo and Neumaier (Graphs Combin 23:713–726, 2007).
Bibliographie:ObjectType-Article-1
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ISSN:0925-9899
1572-9192
DOI:10.1007/s10801-025-01458-8