Peer-reviewedCC BY 4.0Mathematics
On Almost Uniformly Locally Finite Graphs
- 1Moscow Center for Fundamental and Applied Mathematics, Moscow State University, Leninskie Gory 1, Moscow 119991, Russia
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.
Related
- On the embedding rigidity problem for uniformly locally finite coarse spaces
- Least energy sign-changing solutions for asymptotically cubic Kirchhoff equations on locally finite graphs
- Gradient estimates and volume doubling for locally finite weighted graphs with $CDψ(n,-K)$ condition
- Unfriendly partitions of locally finite Borel graphs
- Dirichlet problem on locally finite graphs (revised and extended version)
BibTeX
@article{manuilov2026almost,
title = {{On Almost Uniformly Locally Finite Graphs}},
author = {Vladimir Manuilov},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14193628},
url = {https://www.mdpi.com/2227-7390/14/19/3628},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - On Almost Uniformly Locally Finite Graphs
AU - Vladimir Manuilov
PY - 2026
DA - 2026/10/07
JO - Mathematics
DO - 10.3390/math14193628
UR - https://www.mdpi.com/2227-7390/14/19/3628
AB - 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.
SN - 2227-7390
ER -