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On the structure of matroids arising from the gain graphs

Maimani, H. R ; Sharif University of Technology | 2023

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  1. Type of Document: Article
  2. DOI: 10.1016/j.disc.2023.113637
  3. Publisher: Elsevier B.V , 2023
  4. Abstract:
  5. 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. © 2023 Elsevier B.V
  6. Keywords:
  7. Gain graph ; Generalized Hamming weight ; Matroid ; Signed graph ; Simplicial complex
  8. Source: Discrete Mathematics ; Volume 346, Issue 12 , 2023 ; 0012365X (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0012365X23003230