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Completely rigid graphs
Published online by Cambridge University Press: 09 April 2009
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In general, a structure is called rigid if it admits only the trivial structure preserving transformations. Of course, what is trivial depends on the context. In [7] the authors understand by a rigid graph one which has the property that the only edge preserving transformation of the vertices is the identity map. In other contexts, however, it is convenient to regard the constant maps as trivial also. (See [2] where a topological space is given which admits as continuous transformations only the identity and the constants.) The purpose of this note is to construct graphs rigid in the later sense; we call them completely rigid.
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 18 , Issue 3 , November 1974 , pp. 310 - 317
- Copyright
- Copyright © Australian Mathematical Society 1974
References
[1]Frucht, R., ‘Herstellung von Graphen mit vorgegebener abstrakter Gruppe’, Compos. Math. 6 (1938), 239–250.Google Scholar
[2]De Groot, J., ‘Groups represented by homeomorphism groups, I'’, Math. Annalen 138 (1959), 80–102.CrossRefGoogle Scholar
[3]Hedrlin, Z. and Pultr, A., ‘Symmetric Relations (Undirected Graphs) with Given Semigroups’, Monatsh. Math. 69, (1965), 318–322.CrossRefGoogle Scholar
[5]Pultr, A. and Hedrlin, Z., ‘Relations (Graphs) with Given Infinite Semigroups’, Monatsh. Math. 68 (1964), 421–425.CrossRefGoogle Scholar
[7]Vopenka, P., Pultr, A., and Hedrlin, Z., ‘A Rigid Relation Exists on Any Set’, Comment. Math. Univ. Carolinae 6 (1965), 149–155.Google Scholar
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