A matrix description of weakly bipartitive and bipartitive families

Bankoussou-mabiala, Edward; Boussaïri, Abderrahim; Chaïchaâ, Abdelhak; Chergui, Brahim

doi:10.1016/j.laa.2017.07.025

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The Determinant Of the Join Of Tournaments1

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“…Otherwise, we say that T is switching indecomposable. Switching decomposability coincides with the bijoin decomposability [2,4].…”

Section: The Determinant Of the Join Of Tournamentsmentioning

confidence: 90%

On unimodular tournaments

Belkouche,

Boussaïri,

Chaïchaâ

et al. 2021

Preprint

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A tournament is unimodular if the determinant of its skew-adjacency matrix is 1. In this paper, we give some properties and constructions of unimodular tournaments. A unimodular tournament T with skew-adjacency matrix S is invertible if S −1 is the skew-adjacency matrix of a tournament. A spectral characterization of invertible tournaments is given. Lastly, we show that every n-tournament can be embedded in a unimodular tournament by adding at most n − ⌊log 2 (n)⌋ vertices.

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“…Otherwise, we say that T is switching indecomposable. Switching decomposability coincides with the bijoin decomposability [2,4].…”

Section: The Determinant Of the Join Of Tournamentsmentioning

confidence: 90%