On the structure of matroids arising from the gain graphs

On the structure of matroids arising from the gain graphs

The gain graphs are essential generalizations of the signed graphs. They are indeed directed graphs whose edges are labeled by the elements of a group rather than just ±1. In this paper, we prove the existence of matroids arising from these graphs. Further, we study the structure of the obtained mat...

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Veröffentlicht in:Discrete mathematics 2023-12, Vol.346 (12), p.113637, Article 113637
Hauptverfasser: Maimani, H.R., Parsaei-Majd, L., Pournaki, M.R., Poursoltani, M.
Format: Artikel
Sprache:eng
Schlagworte:
Gain graph
Generalized Hamming weight
Matroid
Signed graph
Simplicial complex
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Zusammenfassung:The gain graphs are essential generalizations of the signed graphs. They are indeed directed graphs whose edges are labeled by the elements of a group rather than just ±1. In this paper, we prove the existence of matroids arising from these graphs. Further, we study the structure of the obtained matroids as well as their relation with the generalized Hamming weights, the regularity of the ideal of circuits, and the codes.
ISSN:0012-365X
DOI:10.1016/j.disc.2023.113637