zbMATH — the first resource for mathematics

Green’s relations on the endomorphism monoid of a graph. (English) Zbl 0853.05046
Summary: Green’s relations on the endomorphism monoid of a graph are explicitly described. In particular, it is revealed that for endomorphism monoids of some special classes of graphs, Green’s relations may possess some distinct combinatorial features.

05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
Full Text: EuDML
[1] HARARY F.: Graph Theory. Addison-Wesley, Reading, 1969. · Zbl 0196.27202
[2] HOWIE J. M.: An Introduction to Semigroup Theory. Academic Press, New York-London, 1976. · Zbl 0355.20056
[3] KNAUER U., NIEPORTE M.: Endomorphisms of graphs I. Arch. Math. (Basel) 52 (1989), 607-614. · Zbl 0683.05026
[4] KNAUER U.: Endomorphisms of graphs II. Arch. Math. (Basel) 55 (1990), 193-203. · Zbl 0683.05027
[5] KNAUER U.: Unretractive and s-unretractive joins and lexicographic products of graphs. J. Graph Theory 11 (1987), 429-440. · Zbl 0659.05055
[6] LI W.-M.: Green’s relations on the strong endomorphism monoid of a graph. Semigroup Forum 47 (1993), 209-214. · Zbl 0791.20077
[7] LI W.-M.: The Structure of the Endomorphism Monoid of a Graph. Ph.D. Thesis, Germany, Universitat Oldenburg, 1993.
[8] MAGILL K. D.: A survey of semigroups of continuous selfmaps. Semigroup Forum 11 (1975/76), 189-282. · Zbl 0338.20088
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.