Matroids of Gain Signed Graphs

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.

13 fig., 46 pp. v2 has new Example 3.7, minor editing, 47 pp. v3 has new Example 3.12, 48 pp