Abstract
In this paper, we explicitly describe all the inverses and pseudo-inverses of a strong endomorphism of a graph. The number of them is determined. In addition, we give a characterization of a strong endomorphism whose pseudo-inverse set coincides with its inverse set. The graph, each strong endomorphism of which has this property, is also investigated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Harary, F., Graph Theory. Addison-Wesley, Reading, 1969.
Howie, J.M., An Introduction to Semigroup Theory. Academic Press, New York-London, 1976.
Knauer, U. and Nieporte, M.,Endomorphisms of graphs I, The monoid of strong endomorphisms, Arch. Math.,52 (1989), 607–614.
Knauer, U.,Endomorphisms of graphs II, Various unretractive graphs, Arch. Math.,55 (1990), 193–203.
Li, W-M.,Green's relations on the strong endomorphism monoid of a graph., Semigroup Forum,47 (1993), 209–214.
Li, W-M.,A regular endomorphism of a graph and its inverses. Mathematika,41 (1994), 189–198.
Nummert, U.A.,The monoid of strict endomorphisms of wreath products of graphs, Math. Notes,41 (1987), 483–490.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Li, W. Inverses and pseudo-inverses of a strong endomorphism of a graph. Acta Mathematica Sinica 11, 372–380 (1995). https://doi.org/10.1007/BF02248747
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02248747