The unraveled ball of radius $r$ centered at a vertex $v$ in a weighted graph $G$ is the ball of radius $r$ centered at $v$ in the universal cover of $G$. We present a general bound on the maximum spectral radius of unraveled balls of fixed radius in a weighted graph. The weighted degree of a vertex in a weighted graph is the sum of weights of edges incident to the vertex. A weighted graph is called regular if the weighted degrees of its vertices are the same. Using the result on unraveled balls, we prove a variation of the Alon–Boppana theorem for regular weighted graphs.
@article{10_37236_12212,
author = {Alexander Polyanskii and Rynat Sadykov},
title = {Alon-Boppana-type bounds for weighted graphs},
journal = {The electronic journal of combinatorics},
year = {2024},
volume = {31},
number = {1},
doi = {10.37236/12212},
zbl = {1543.05073},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12212/}
}
TY - JOUR
AU - Alexander Polyanskii
AU - Rynat Sadykov
TI - Alon-Boppana-type bounds for weighted graphs
JO - The electronic journal of combinatorics
PY - 2024
VL - 31
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/12212/
DO - 10.37236/12212
ID - 10_37236_12212
ER -
%0 Journal Article
%A Alexander Polyanskii
%A Rynat Sadykov
%T Alon-Boppana-type bounds for weighted graphs
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/12212/
%R 10.37236/12212
%F 10_37236_12212
Alexander Polyanskii; Rynat Sadykov. Alon-Boppana-type bounds for weighted graphs. The electronic journal of combinatorics, Tome 31 (2024) no. 1. doi: 10.37236/12212
