Let $\Gamma$ denote a finite, simple and connected graph. Fix a vertex $x$ of $\Gamma$ and let $T=T(x)$ denote the Terwilliger algebra of $\Gamma$ with respect to $x$. In this paper we study the unique irreducible $T$-module with endpoint $0$. We assume that this $T$-module is thin. The main result of the paper is a combinatorial characterization of this property.
@article{10_37236_10950,
author = {Blas Fern\'andez and \v{S}tefko Miklavi\v{c}},
title = {On the trivial {\(T\)-module} of a graph},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {2},
doi = {10.37236/10950},
zbl = {1492.05065},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10950/}
}
TY - JOUR
AU - Blas Fernández
AU - Štefko Miklavič
TI - On the trivial \(T\)-module of a graph
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/10950/
DO - 10.37236/10950
ID - 10_37236_10950
ER -
%0 Journal Article
%A Blas Fernández
%A Štefko Miklavič
%T On the trivial \(T\)-module of a graph
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/10950/
%R 10.37236/10950
%F 10_37236_10950
Blas Fernández; Štefko Miklavič. On the trivial \(T\)-module of a graph. The electronic journal of combinatorics, Tome 29 (2022) no. 2. doi: 10.37236/10950
