Matroids of Gain Signed Graphs
Combinatorics
2022-06-22 v3
Abstract
A signed graph has edge signs. A gain graph has oriented edge gains drawn from a group. We define the combination of the two for the abelian case, in which each oriented edge of a signed graph has a gain from an abelian group, concentrating on the case of the additive group of a field. We develop the elementary graph properties, the associated matroid, and the vector and hyperplanar representations.
Keywords
Cite
@article{arxiv.2206.00237,
title = {Matroids of Gain Signed Graphs},
author = {Laura Anderson and Ting Su and Thomas Zaslavsky},
journal= {arXiv preprint arXiv:2206.00237},
year = {2022}
}
Comments
13 fig., 46 pp. v2 has new Example 3.7, minor editing, 47 pp. v3 has new Example 3.12, 48 pp