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RUP
FAMNIT - Faculty of Mathematics, Science and Information Technologies
FHŠ - Faculty of Humanities
FM - Faculty of Management
FTŠ Turistica - Turistica – College of Tourism Portorož
FVZ - Faculty of Health Sciences
IAM - Andrej Marušič Institute
PEF - Faculty of Education
UPR - University of Primorska
ZUP - University of Primorska Press
COBISS
University of Primorska, University Library - all departments
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Title:
Uniform equations for bipartite graphs and the center of a Terwilliger algebra
Authors:
ID
Miklavič, Štefko
(
Author
)
ID
Monzillo, Giusy
(
Author
)
Files:
RAZ_Miklavic_Stefko_2026.pdf
(966,73 KB)
MD5: 601CBCC924EC4698183EC42053C90A10
https://www.sciencedirect.com/science/article/pii/S0024379526001837
Language:
English
Work type:
Article
Typology:
1.01 - Original Scientific Article
Organization:
IAM - Andrej Marušič Institute
Abstract:
The uniform property was introduced by P. Terwilliger in the context of graded posets and was later extended to connected bipartite graphs. The core of this definition involves the so called uniform equations that must be satisfied. Let Γ denote a connected bipartite graph. Fix a vertex x of Γand let T=T(x) denote the corresponding Terwilliger algebra. In this paper, we study the connections between the uniform equations and the center of T. We show that these uniform equations give rise to a certain subspace of the center of T. Changing the logical direction, we show that if a matrix of a particular form belongs to the center of T, then uniform equations are satisfified.
Keywords:
uniform equations
,
center of a Terwilliger algebra
,
bipartite graphs
Publication version:
Version of Record
Publication date:
27.04.2026
Year of publishing:
2026
Number of pages:
str. 30-52
Numbering:
Vol. 744
PID:
20.500.12556/RUP-23030
UDC:
519.17
ISSN on article:
0024-3795
DOI:
10.1016/j.laa.2026.04.024
COBISS.SI-ID:
277454339
Publication date in RUP:
08.05.2026
Views:
190
Downloads:
7
Metadata:
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Record is a part of a journal
Title:
Linear algebra and its applications
Shortened title:
Linear algebra appl.
Publisher:
North Holland
ISSN:
0024-3795
COBISS.SI-ID:
1119247
Document is financed by a project
Funder:
ARIS - Slovenian Research and Innovation Agency
Project number:
P1-0285-2022
Name:
Algebra, diskretna matematika, verjetnostni račun in teorija iger
Funder:
ARIS - Slovenian Research and Innovation Agency
Project number:
J1-3003-2021
Name:
Grupe, poseti, in kompleksi
Funder:
ARIS - Slovenian Research and Innovation Agency
Project number:
J1-4008-2022
Name:
Drevesno neodvisnostno število grafov
Funder:
ARIS - Slovenian Research and Innovation Agency
Project number:
J1-4084-2022
Name:
Določeni kombinatorični objekti v spektralni domeni - križiščna analiza
Funder:
ARIS - Slovenian Research and Innovation Agency
Project number:
J1-50000-2023
Name:
Hamiltonski cikli z rotacijsko simetrijo v povezanih točkovno tranzitivnih grafih
Funder:
ARIS - Slovenian Research and Innovation Agency
Project number:
J1-60012-2025
Name:
“Linearne kode preko posebnih razredov funkcij - relacije in načrtovanje
Funder:
ARIS - Slovenian Research and Innovation Agency
Project number:
N1-0353-2024
Name:
Nekatere uporabe t-točkovnega štetja v algebraični in kombinatorični teoriji grafov z vidika asociacijskih shem
Funder:
ARIS - Slovenian Research and Innovation Agency
Project number:
N1-0428-2025
Name:
Razširitve Erdös-Ko-Rado izreka na tranzitivne permutacijske grupe
Funder:
ARIS - Slovenian Research and Innovation Agency
Project number:
N1-0429-2025
Name:
Visokodimenzionalna delovanja klasičnih grup v Galoisovi geometriji
Funder:
ARIS - Slovenian Research and Innovation Agency
Project number:
N1-0391-2025
Name:
Pretok celih števil skozi točkovno-tranzitivne grafe: Študija simetrije v grafih
Funder:
ARIS - Slovenian Research and Innovation Agency
Project number:
N1-0409-2025
Name:
Asociacijske sheme, avtomati in incidenčne strukture
Licences
License:
CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Link:
http://creativecommons.org/licenses/by-nc-nd/4.0/
Description:
The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.
Secondary language
Language:
Slovenian
Abstract:
Uniformno lastnost je prvi definiral P. Terwilliger v kontekstu gradiranih delno urejenih množic. Definicija je bila kasneje razširjena na povezane dvodelne grafe. Jedro te definicije so tako imenovane uniformne enačbe, ki morajo biti izpolnjene. Naj bo Γ povezan dvodelen graf. Fiksirajmo vozlišče x grafa Γ in naj bo T=T(x) pripadajoča Terwilligerjeva algebra. V tem članku študiramo povezave med uniformnimi enačbami in centrom algebre T. Pokažemo, da te uniformne enačbe porodijo določen podprostor centra algebre T. Pokažemo tudi, da če center algebre T vsebuje matriko ki je določene oblike, potem so uniformne enačbe izpolnjene.
Keywords:
uniformne enačbe
,
center Terwilligerjeve algebre
,
dvodelni grafi
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