On a certain class of 1-thin distance-regular graphs
MacLean, Mark ; Miklavič, Štefko
Naj bo ▫$\Gamma$▫ ne-dvodelen razdaljno-regularen graf z množico vozlišč ▫$X$▫, premerom ▫$D \ge 3$▫, ter stopnjo ▫$k \ge 3$▫. Izberimo si vozlišče ▫$x \in X$▫ in naj bo ▫$T=T(x)$▫ Terwilligerjeva ...algebra grafa ▫$\Gamma$▫ glede na ▫$x$▫. Za vsako vozlišče ▫$z \in X$▫ in za ▫$0 \le i \le D$▫ naj bo ▫$\Gamma_i(z)=\{w \in X : \partial(z, w) = i\}$▫ označimo ▫$D_j^i = D_j^i(x, y) = \Gamma_i(x) \cap \Gamma_j(y)$▫ in za dano vozlišče ▫$y$▫ definirajmo preslikavi ▫$H_i \colon D_i^i \to \mathbb{Z}$▫ in ▫$V_i \colon D_{i-1}^i \to \mathbb{Z}$▫ takole: ▫$$H_i(z) = |\Gamma_1(z) \cap D_{i-1}^{i-1}|, \quad V_i(z) = |\Gamma_1(z) \cap D_{i-1}^{i-1}|.$$▫ Privzemimo, da sta za vsako vozlišče ▫$y \in \Gamma_1(x)$▫ in za vsak ▫$2 \le i \le D$▫ pripadajoči preslikavi ▫$H_i$▫ in ▫$V_i$▫ konstantni, ter da te konstante niso odvisne od izbire vozlišča ▫$y$▫. Dalje tudi privzemimo, da so konstantne vrednosti preslikav ▫$H_i$▫ neničelne za ▫$2 \le i \le D$▫. Pokažemo, da je vsak nerazcepen ▫$T$▫-modul s krajiščem 1 tanek. Nadalje tudi pokažemo, da ima ▫$\Gamma$▫ do izomorfizma natančno natanko tri nerazcepne ▫$T$▫-module s krajiščem 1 natanko takrat, ko veljajo trije kombinatorični pogoji (ki jih definiramo kasneje). Kot primer pokažemo, da ti trije kombinatorični pogoji veljajo za Johnsonove grafe ▫$J(n, m)$▫, kjer je ▫$n \ge 7$▫, ▫$3 \le m < n/2$▫.
It was not necessary to add the material to the shelf.
Bibliographic material was successfully added on shelf.
Adding bibliographical material on shelf was not successful.
Material is already on the shelf.
Permalink
URL:
Impact factor
Access to the JCR database is permitted only to users from Slovenia. Your current IP address is not on the list of IP addresses with access permission, and authentication with the relevant AAI accout is required.
Year
Impact factor
Edition
Category
Classification
JCR
SNIP
JCR
SNIP
JCR
SNIP
JCR
SNIP
Select the library membership card:
DRS,
in which the journal is indexed
Database name
Field
Year
Links to authors' personal bibliographies
Links to information on researchers in the SICRIS system
Subject headings in COBISS General List of Subject Headings
Select pickup location
The material from the parent unit is free. If the material is delivered to the pickup location from another unit, the library may charge you for this service.
PDF
