Subgroup Switching of Skew Gain Graphs

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Gain graphs are graphs in which each edge has a gain (a label from a group so that reversing the direction of an edge inverts the gain). In this paper we take a generalized view of gain graphs in which the gain of an edge is related to the gain of the reverse edge by an anti-involution, i.e., an anti-automorphism of order at most two. We call these skew gain graphs. Switching is an operation that transforms one skew gain graph into another, driven by a selector that selects an element of some group Γ in each of its vertices. In this paper, we investigate a generalization of this model, in which we insist that in each vertex v the selected elements are taken from a subgroup Γv of Γ. We call this operation subgroup switching. Our main interest in this paper is in establishing which properties of the theory of switching classes of the skew gain graphs carry over to subgroup switching classes, and which do not.
Original languageEnglish
Pages (from-to)111-122
Number of pages12
JournalFundamenta Informaticae
Issue number1-4
Publication statusPublished - Jan 2012


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