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Enumeration of weak isomorphism classes of signed graphs

✍ Scribed by Tadeusz Sozański

Publisher
John Wiley and Sons
Year
1980
Tongue
English
Weight
869 KB
Volume
4
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

A signed graph is a graph in which each line has a plus or minus sign. Two signed graphs are said to be weakly isomorphic if their underlying graphs are isomorphic through a mapping under which signs of cycles are preserved, the sign of a cycle being the product of the signs of its lines. Some enumeration problems implied by such a definition, including the problem of self‐dual configurations, are solved here for complete signed graphs by methods of linear algebra over the two‐element field. It is also shown that weak isomorphism classes of complete signed graphs are equal in number to other configurations: unlabeled even graphs, two‐graphs and switching classes.

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