A mathematical bibliography of signed and gain graphs and allied areas
A ``signed graph'' is a graph with signs labelling its edges. A ``gain graph'' has elements of any group as edge labels (called ``gains''), with the understanding that reversing the sense in which one traverses the edge will invert the gain. In a ``bidirected graph'', both ends of each edge are directed independently; it can be regarded as an oriented signed graph. A ``biased graph'' is a combinatorial generalization of signed and gain graphs. The topics engaged by signed and gain graph theory include signed digraphs, Dowling lattices, combinatorics of root systems, ``braid'' and ``Shi'' and related arrangements of hyperplanes, parity of cycles and paths and max-cut problems (which in effect concern all-negative signatures), generalized networks (networks with gains), qualitative matrix theory, quadratic pseudo-Boolean functions, dynamic labeled 2-structures, and applications to social science (psychology, sociology, anthropology, economics) and natural science (physics, chemistry, biology). The literature is vast, scattered, and diverse. The bibliography is a classified and copiously annotated list of nearly 900 publications (and suitable unpublished manuscripts, theses, etc.) of mathematical interest related to signed graphs, vertex-signed graphs, gain graphs, and bidirected graphs. The annotations, some of which are very detailed, include descriptions, commentary, cross references, and dozens of reasearch problems. Furthermore, the entries are classified by short codes into some three dozen topical areas. The glossary (see Zbl 0898.05002) is a list of all the terms that I have been able to collect thus far, that are used with signed and gain graphs and related mathematics, including applications. Due to the breadth of the literature there are many concepts, often having multiple names, and the diversity and inconsistency of the terminology is great. The glossary tries to list all the terminology in frequent or infrequent use; and, in some cases, to establish at least a little uniformity, such as by suggesting preferred terminology (normally, the more common, clearly descriptive, or distinctive terms).
scientific article; zbMATH DE number 1179151