Work

On Almost Uniformly Locally Finite Graphs

Year: 2026

Type: article

Abstract: We study locally finite graphs whose normalized adjacency operators belong to the C*-algebra T, the norm closure of the algebra of l1-bounded operators. We give sufficient and necessary conditions in terms of the degrees of adjacent vertices, prove stability results under finite edge perturbations and Cartesian products, and compute several examples: regular graphs, complete bipartite graphs, complete graphs with pendant leaves, subdivisions, and spherically homogeneous trees. These examples show that T-uniformity is a weak regularity condition which forbids vertices of large degree from being adjacent to too many vertices of much smaller degree.

Source: Mathematics

DOI: 10.3390/math14193628

Author: Vladimir Manuilov

Institutions: Lomonosov Moscow State University, Moscow Center of Fundamental and Applied Mathematics

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

OpenAlex ID: W7221017027

FWCI:

Cites: 5

Cited by:

Related to: 10