Preserving λ-scrambling Matrices

• Autorzy: Guterman A. E. , Maksaev A. M.

Identyfikatory

DOI

10.3233/FI-2018-1717

• Konferencja: RuFiDiM Conference, Russian-Finnish Symposium in Discrete Mathematics (5; 16-19.05. 2017; Turku; Finland)
• Języki publikacji: EN

Abstrakty

EN

The notion of scrambling index was firstly introduced by Akelbek and Kirkland in 2009. For a primitive digraph D, it is defined as the smallest positive integer k such that for every pair of vertices u and v of D there exist two directed paths of lengths k to a common vertex w. This notion turned out to be useful for several applications, e. g., to estimate eigenvalues of non-negative primitive stochastic matrices. In 2010 Huang and Liu with the background of a memoryless communication system generalized this notion to λ-tuples of vertices and named it λ-th upper scrambling index. These notions can be reformulated in terms of matrix theory. A standard way to generate matrices with the given λ-th upper scrambling index is to apply certain matrix transformations that preserve this index to the existing examples of matrices with known λ-th upper scrambling index. In this paper we completely characterize bijective linear maps preserving λ-th upper scrambling index 1 or 0.

Słowa kluczowe

EN

scrambling matrix; scrambling index; directed graphs; nonnegative matrices

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2018
• Tom: Vol. 162, nr 2/3
• Strony: 119--141
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

Guterman A. E.

• Lomonosov Moscow State University, 119991, Moscow, Russia
• Moscow Center for Continuous Mathematical Education, 119002, Moscow, Russia
• Moscow Institute of Physics and Technology, 141701, Dolgoprudny, Russia

autor

Maksaev A. M.

• Lomonosov Moscow State University, 119991, Moscow, Russia
• Moscow Center for Continuous Mathematical Education, 119002, Moscow, Russia
• Moscow Institute of Physics and Technology, 141701, Dolgoprudny, Russia

Bibliografia

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