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Endomorphisms of graphs. II: Various unretractive graphs. (English) Zbl 0683.05027
In this part of the article [part I, cf. the review above] graphs are investigated, for which different endomorphism monoids coincide. Here endomorphisms, strong endomorphisms and automorphisms are considered. Coincidences are investigated for joins and lexicographic products of graphs. There are lists of graphs with the respective properties up to 8 vertices in two cases and up to 5 vertices in the remaining case.
Reviewer: U.Knauer

MSC:
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
20M20 Semigroups of transformations, relations, partitions, etc.
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[1] H.Ahrends, Endomorphismenmonoide von Graphen und Distributivgesetze f?r Kompositionen von Graphen. Diplomarbeit, Oldenburg 1987.
[2] F.Harary, Graph Theory. Reading 1969; deutsch: M?nchen 1974.
[3] Z. Hedrlin andA. Pultr, On rigid undirected graphs. Canad. J. Math.18, 1237-1242 (1966). · Zbl 0145.20603
[4] P. Hell, Rigid undirected graphs with given number of vertices. Comment. Math. Univ. Carolinae9, 51-59 (1968). · Zbl 0167.22101
[5] P.Hell and J.Nesetril, Absolute retracts in graphs. In: Graphs and Combinatorics, Eds. R. A. Bari and F. Harary, LNM406, 291-301, Berlin-Heidelberg-New York 1974.
[6] U. Knauer, Unretractive and S-unretractive joins and lexicographic products of graphs. J. Graph Theory (3)11, 429-440 (1987). · Zbl 0659.05055
[7] U. Knauer andM. Nieporte, Endomorphisms of graphs, I. The monoid of strong endomorphisms. Arch. Math.52, 607-614 (1989). · Zbl 0683.05026
[8] U. Nummert, On the monoid of strong endomorphisms of wreath products of graphs (Russian,translated into English). Mat. Zametki41, 844-853 (1987).
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