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A regular endomorphism of a graph and its inverses

Published online by Cambridge University Press:  26 February 2010

Weimin Li
Affiliation:
Fachbereich Mathematik, Universität Oldenburg, 26111 Oldenburg, Germany.
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Abstract

In this paper, we first give a characterization of a regular endomorphism of a graph. Then, we explicitly describe its inverses through idempotents.

Type
Research Article
Copyright
Copyright © University College London 1994

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References

1.Harary, F.. (1969) Graph Theory (Addison-Wesley, Reading, 1969).Google Scholar
2.Howie, J. M.. An. introduction to semigroup theory (New York-London, 1976).Google Scholar
3.Knauer, U and Nieporte, M.. Endomorphisms of graphs I, The monoid of strong endomorphisms. Arch. Math., 52 (1989), 607614.CrossRefGoogle Scholar
4.Knauer, U. Endomorphisms of graphs II, Various unretractive graphs. Arch. Math., 55 (1990), 193203.CrossRefGoogle Scholar
5.Li, W-M.Green's relations on the endomorphoism monoids of graphs.SubmittedGoogle Scholar
6.Miller, D.D and Clifford, A. H.. Regular O-classes in semigroups. Trans. Amer. Math. Soc., 82 (1956), 270280.Google Scholar
7.Wilkeit, E. Endormorphisms of graphs III, Graphs with a regular monoid. Submitted.Google Scholar
8.Problems raised at the problem session of the Colloquium on Semigroups in Szeged, August 1987. Semigroup Forum, 37 (1988), 367373.Google Scholar