✦ LIBER ✦

Graph generators

✍ Scribed by Milan Randić; Wayne L. Woodworth; Alexander F. Kleiner; Haruo Hosoya

Publisher: John Wiley and Sons
Year: 1987
Tongue: English
Weight: 942 KB
Volume: 8
Category: Article
ISSN: 0192-8651
DOI: 10.1002/jcc.540080433

No coin nor oath required. For personal study only.

✦ Synopsis

We consider the construction of highly symmetrical vertex transitive graphs. Some such graphs represent the degenerate rearrangements in which a molecule or an ion is formed by breaking and making bonds so that the final and the initial skeleton is identical. The approach is closely related to Cayley's graphs for selected groups. We restrict the choice of generators to symmetric matrices. Successive multiplications of such matrices generate other permutation matrices of the same dimension, each new matrix representing a new vertex for a transitive graph under the construction. In particular we restrict our discussion to matrices of dimension 3 and 4 and proceed to construct systematically all transitive graphs using 4 x 4 symmetric matrices as generators.

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