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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: 663; Prenosov: 25
.pdf Celotno besedilo (325,02 KB)

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On minimal forbidden subgraphs for the class of EDM-graphs
Gašper Jaklič, Jolanda Modic, 2015, izvirni znanstveni članek

Opis: In this paper, a relation between graph distance matrices and Euclidean distance matrices (EDM) is considered. Graphs, for which the distance matrix is not an EDM (NEDM-graphs), are studied. All simple connected non-isomorphic graphs on ▫$n \le 8$▫ nodes are analysed and a characterization of the smallest NEDM-graphs, i.e., the minimal forbidden subgraphs, is given. It is proven that bipartite graphs and some subdivisions of the smallest NEDM-graphs are NEDM-graphs, too.
Ključne besede: graph theory, graph, Euclidean distance matrix, distance, eigenvalue
Objavljeno v RUP: 31.12.2021; Ogledov: 860; Prenosov: 18
.pdf Celotno besedilo (711,65 KB)

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Commuting graphs and extremal centralizers
Gregor Dolinar, Aleksandr Èmilevič Guterman, Bojan Kuzma, Polona Oblak, 2014, izvirni znanstveni članek

Opis: We determine the conditions for matrix centralizers which can guarantee the connectedness of the commuting graph for the full matrix algebra ▫$M_n(\mathbb{F})$▫ over an arbitrary field ▫$\mathbb{F}$▫. It is known that if ▫$\mathbb{F}$▫ is an algebraically closed field and ▫$n \ge 3$▫, then the diameter of the commuting graph of ▫$M_n(\mathbb{F})$▫ is always equal to four. We construct a concrete example showing that if ▫$\mathbb{F}$▫ is not algebraically closed, then the commuting graph of ▫$M_n(\mathbb{F})$▫ can be connected with the diameter at least five.
Ključne besede: commuting graph, matrix ring, centralizer
Objavljeno v RUP: 31.12.2021; Ogledov: 725; Prenosov: 22
.pdf Celotno besedilo (228,78 KB)

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A note on homomorphisms of matrix semigroup
Matjaž Omladič, Bojan Kuzma, 2013, izvirni znanstveni članek

Opis: Let ▫$\mathbb{F}$▫ be a field. We classify multiplicative maps from ▫${\mathcal M}_n(\mathbb{F})$▫ to ▫${\mathcal M}_{n \choose k}(\mathbb{F})$▫ which annihilate a zero matrix and map rank-▫$k$▫ matrix into a rank-one matrix.
Ključne besede: matrix semigroup, homomorphism, representation
Objavljeno v RUP: 31.12.2021; Ogledov: 695; Prenosov: 18
.pdf Celotno besedilo (247,09 KB)

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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: 989; Prenosov: 24
URL Povezava na celotno besedilo

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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: 834; Prenosov: 28
.pdf Celotno besedilo (265,78 KB)

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