Signed Graphs and Geometry

Abstract

These lecture notes are a personal introduction to signed graphs, concentrating on the aspects that have been most persistently interesting to me. They are just a few corners of signed graph theory; I am leaving out a great deal. The emphasis is on the way signed graphs arise naturally from geometry, especially from the geometry of the classical root systems. Most of the properties I discuss generalize those of unsigned graphs, but the constructions and proofs are often more complicated. My aim is a coherent presentation of the subject, with a few illustrative proofs and adequate references. Hence the arrangement of the notes is topical with only occasional remarks about the historical course of development. Though this is mainly an expository survey, some of the results have not hitherto been published.

33 pp., many figures. Presented at the International Workshop on Set-Valuations, Signed Graphs, Geometry and Their Applications (IWSSG-2011), Mananthavady, Kerala, India, Sept., 2011

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• Minimum $T$-Joins and Signed-Circuit Covering
• Some New Results on Integer Additive Set-Valued Signed Graphs
• A Study on Set-Valuations of Signed Graphs
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• Hajós-like theorem for signed graphs