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Acyclicity of Switching Classes

✍ Scribed by J. Hage; T. Harju

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
133 KB
Volume
19
Category
Article
ISSN
0195-6698

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✦ Synopsis

For a finite undirected graph G = (V, E) and a subset A βŠ† V , the vertex switching of G by A is defined as the graph G A = (V, E ), which is obtained from G by removing all edges between A and its complement A and adding as edges all nonedges between A and A. The switching class [G] determined by G consists of all vertex switchings G A for subsets A βŠ† V . We prove that the trees of a switching class [G] are isomorphic to each other. We also determine the types of trees T that have isomorphic copies in [G]. Finally we show that apart from one exceptional type of forest, the real forests in a switching class are isomorphic. Here a forest is real, if it is disconnected.

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