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1.
On [plus/minus] 1 eigenvectors of graphs
Dragan Stevanović, 2016, izvirni znanstveni članek

Opis: While discussing his spectral bound on the independence number of a graph, Herbert Wilf asked back in 1986 what kind of a graph admits an eigenvector consisting solely of ▫$\pm 1$▫ entries? We prove that Wilf's problem is NP-complete, but also that the set of graphs having a ▫$\pm 1$▫ eigenvector is quite rich, being closed under a number of different graph compositions.
Ključne besede: eigenvector, adjacency matrix, Wilf's problem
Objavljeno v RUP: 03.01.2022; Ogledov: 653; Prenosov: 25
.pdf Celotno besedilo (325,02 KB)

2.
On 12-regular nut graphs
Nino Bašić, Martin Knor, Riste Škrekovski, 2021, izvirni znanstveni članek

Ključne besede: nut graph, adjacency matrix, singular matrix, core graph, Fowler construction, regular graph
Objavljeno v RUP: 16.07.2021; Ogledov: 973; Prenosov: 24
URL Povezava na celotno besedilo

3.
An alternate proof of the monotonicity of the number of positive entries in nonnegative matrix powers
Slobodan Filipovski, 2021, izvirni znanstveni članek

Ključne besede: digraphs, monotonicity, adjacency matrix
Objavljeno v RUP: 04.02.2021; Ogledov: 822; Prenosov: 28
.pdf Celotno besedilo (265,78 KB)

4.
5.
Adjacency preservers, symmetric matrices, and cores
Marko Orel, 2012, izvirni znanstveni članek

Opis: It is shown that the graph ▫$\Gamma_n$▫ that has the set of all ▫$n \times n$▫ symmetric matrices over a finite field as the vertex set, with two matrices being adjacent if and only if the rank of their difference equals one, is a core if ▫$n \ge 3$▫. Eigenvalues of the graph ▫$\Gamma_n$▫ are calculated as well.
Ključne besede: adjacency preserver, symmetric matrix, finite field, eigenvalue of a graph, coloring, quadratic form
Objavljeno v RUP: 15.10.2013; Ogledov: 3035; Prenosov: 141
URL Povezava na celotno besedilo

6.
Q-polynomial distance-regular graphs with a [sub] 1 [equal] 0 and a [sub] 2 [not equal] 0
Štefko Miklavič, 2008, izvirni znanstveni članek

Opis: Let ▫$\Gamma$▫ denote a ▫$Q$▫-polynomial distance-regular graph with diameter ▫$D \ge 3$▫ and intersection numbers ▫$a_1=0$▫, ▫$a_2 \ne 0$▫. Let ▫$X$▫ denote the vertex set of ▫$\Gamma$▫ and let ▫$A \in {\mathrm{Mat}}_X ({\mathbb{C}})$▫ denote the adjacency matrix of ▫$\Gamma$▫. Fix ▫$x \in X$▫ and let denote $A^\ast \in {\mathrm{Mat}}_X ({\mathbb{C}})$ the corresponding dual adjacency matrix. Let ▫$T$▫ denote the subalgebra of ▫$A{\mathrm{Mat}}_X ({\mathbb{C}})$▫ generated by ▫$A$▫, ▫$A^\ast$▫. We call ▫$T$▫ the Terwilliger algebra of ▫$\Gamma$▫ with respect to ▫$x$▫. We show that up to isomorphism there exists a unique irreducible ▫$T$▫-module ▫$W$▫ with endpoint 1. We show that ▫$W$▫ has dimension ▫$2D-2$▫. We display a basis for ▫$W$▫ which consists of eigenvectors for ▫$A^\ast$▫. We display the action of ▫$A$▫ on this basis. We show that ▫$W$▫ appears in the standard module of ▫$\Gamma$▫ with multiplicity ▫$k-1$▫, where ▫$k$▫ is the valency of ▫$\Gamma$▫.
Ključne besede: mathematics, graph theory, adjacency matrix, distance-regular graph, Terwilliger algebra
Objavljeno v RUP: 15.10.2013; Ogledov: 4168; Prenosov: 30
URL Povezava na celotno besedilo

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