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Electronic Journal of Combinatorics
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A Mathematical Bibliography of Signed and Gain Graphs and Allied Areas

A mathematical bibliography of signed and gain graphs and allied areas
Authors: Thomas Zaslavsky;

A Mathematical Bibliography of Signed and Gain Graphs and Allied Areas

Abstract

A signed graph is a graph whose edges are labeled by signs. This is a bibliography of signed graphs and related mathematics.Several kinds of labelled graph have been called "signed" yet are mathematically very different. I distinguish four types:Group-signed graphs: the edge labels are elements of a 2-element group and are multiplied around a polygon (or along any walk). Among the natural generalizations are larger groups and vertex signs.Sign-colored graphs, in which the edges are labelled from a two-element set that is acted upon by the sign group: - interchanges labels, + leaves them unchanged. This is the kind of "signed graph" found in knot theory. The natural generalization is to more colors and more general groups — or no group.Weighted graphs, in which the edge labels are the elements +1 and -1 of the integers or another additive domain. Weights behave like numbers, not signs; thus I regard work on weighted graphs as outside the scope of the bibliography — except (to some extent) when the author calls the weights "signs".Labelled graphs where the labels have no structure or properties but are called "signs" for any or no reason. 

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Keywords

max-cut, gain graphs, arrangements of hyperplanes, paths, cycles, bibliography, pseudo-Boolean functions, Graph theory, Dowling lattices, General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to combinatorics, networks, matrix theory, terminology, combinatorics of root systems, glossary, signed digraphs, signed graphs, bidirected graphs

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
135
Top 10%
Top 1%
Top 0.1%
gold