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1.
On the Terwilliger algebra of bipartite distance-regular graphs with [Delta][sub]2 = 0 and c[sub]2=1
Mark MacLean, Štefko Miklavič, Safet Penjić, 2016, izvirni znanstveni članek

Opis: Let ▫$\Gamma$▫ denote a bipartite distance-regular graph with diameter ▫$D \geq 4$▫ and valency ▫$k \geq 3$▫. Let ▫$X$▫ denote the vertex set of ▫$\Gamma$▫, and let ▫$A$▫ denote the adjacency matrix of ▫$\Gamma$▫. For ▫$x \in X$▫ and for ▫$0 \leq i \leq D$▫, let ▫$\operatorname{\Gamma}_i(x)$▫ denote the set of vertices in ▫$X$▫ that are distance ▫$i$▫ from vertex ▫$x$▫. Define a parameter ▫$\operatorname{\Delta}_2$▫ in terms of the intersection numbers by ▫$\operatorname{\Delta}_2 = (k - 2)(c_3 - 1) -(c_2 - 1) p_{22}^2$▫. We first show that ▫$\operatorname{\Delta}_2 = 0$▫ implies that ▫$D \leq 5$▫ or ▫$c_2 \in \{1, 2 \}$▫. For ▫$x \in X$▫ let ▫$T = T(x)$▫ denote the subalgebra of ▫$\text{Mat}_X(\mathbb{C})$▫ generated by ▫$A, E_0^\ast, E_1^\ast, \ldots, E_D^\ast$▫, where for ▫$0 \leq i \leq D$, $E_i^\ast$▫ represents the projection onto the▫ $i$▫th subconstituent of ▫$\Gamma$▫ with respect to ▫$x$▫. We refer to ▫$T$▫ as the Terwilliger algebra of ▫$\Gamma$▫ with respect to ▫$x$▫. By the endpoint of an irreducible ▫$T$▫-module ▫$W$▫ we mean ▫$\min \{i | E_i^\ast W \ne 0 \}$▫. In this paper we assume ▫$\Gamma$▫ has the property that for ▫$2 \leq i \leq D - 1$▫, there exist complex scalars ▫$\alpha_i$▫, ▫$\beta_i$▫ such that for all ▫$x, y, z \in X$▫ with ▫$\partial(x, y) = 2$▫, ▫$\partial(x, z) = i$▫, ▫$\partial(y, z) = i$▫, we have ▫$\alpha_i + \beta_i | \operatorname{\Gamma}_1(x) \cap \operatorname{\Gamma}_1(y) \cap \operatorname{\Gamma}_{i - 1}(z) | = | \operatorname{\Gamma}_{i - 1}(x) \cap \operatorname{\Gamma}_{i - 1}(y) \cap \operatorname{\Gamma}_1(z) |$▫. We additionally assume that▫ $\operatorname{\Delta}_2 = 0$▫ with ▫$c_2 = 1$▫. Under the above assumptions we study the algebra ▫$T$▫. We show that if ▫$\Gamma$▫ is not almost 2-homogeneous, then up to isomorphism there exists exactly one irreducible ▫$T$▫-module with endpoint 2. We give an orthogonal basis for this ▫$T$▫-module, and we give the action of ▫$A$▫ on this basis.
Najdeno v: ključnih besedah
Povzetek najdenega: ...$E_i^\ast$▫ represents the projection onto the▫ $i$▫th subconstituent of ▫$\Gamma$▫ with respect to ▫$x$▫. We...
Ključne besede: distance-regular graphs, terwilliger algebra, subconstituent algebra
Objavljeno: 14.11.2017; Ogledov: 519; Prenosov: 39
URL Polno besedilo (0,00 KB)

2.
An A-invariant subspace for bipartite distance-regular graphs with exactly two irreducible T-modules with endpoint 2, both thin
Mark MacLean, Štefko Miklavič, Safet Penjić, 2018, izvirni znanstveni članek

Najdeno v: ključnih besedah
Povzetek najdenega: ...distance-regular graph, Terwilliger algebra, subconstituent algebra, A-invariant subspace...
Ključne besede: distance-regular graph, Terwilliger algebra, subconstituent algebra, A-invariant subspace
Objavljeno: 02.03.2018; Ogledov: 394; Prenosov: 33
URL Polno besedilo (0,00 KB)

3.
O Terwilligerjevi algebri dvodelnih razdaljno-regularnih grafov
Safet Penjić, 2019, doktorska disertacija

Najdeno v: ključnih besedah
Povzetek najdenega: ...bipartite distance-regular graph, Terwilliger algebra, subconstituent algebra, Q-polynomial property, equitable partition...
Ključne besede: bipartite distance-regular graph, Terwilliger algebra, subconstituent algebra, Q-polynomial property, equitable partition
Objavljeno: 04.06.2019; Ogledov: 326; Prenosov: 7
URL Polno besedilo (0,00 KB)

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