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Unretractive and S-unretractive joins and lexicographic products of graphs. (English) Zbl 0659.05055
From the author’s abstract: “Graphs without proper endomorphisms are the subject of this article. It is shown that the join of two graphs has this property if and only if both summands have it, and that the lexicographic product of a complete graph or an odd circuit as first factors has the property if and only if the second factor has it. A somewhat stronger theorem is proved if the lexicographic product has no proper strong endomorphism. The corresponding result for the join is the same as for usual endomorphism.”
Reviewer: R.L.Hemminger

05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C99 Graph theory
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[1] Antohe, Bul. Univ. Galati pp 15– (1978)
[2] Čulik, Casopis Pešt. Mat. 83 pp 133– (1958)
[3] Frucht, Compositio Math. 9 pp 239– (1938)
[4] Graphentheorie I. Wissenschaftliche Buchgesellschaft, Darmstadt (1980).
[5] Graph Theory. Addison-Wesley, Reading, MA (1969).
[6] Hedrlin, Canad. J. Math. 18 pp 1237– (1966) · Zbl 0145.20603
[7] and , Absolute retracts in graphs. In Graphs and Combinatorics, Lecture Notes in Mathematics 406, Eds. and , Springer, Berlin (1974) 291–301.
[8] Hell, Math. Nachr. 87 pp 53– (1979)
[9] An Introduction to Semigroup Theory. Academic Press, London (1976). · Zbl 0355.20056
[10] Knauer, Semigroup Forum 19 pp 177– (1980)
[11] Pultr, Monatsh. Math. 69 pp 318– (1965)
[12] Sabidussi, Duke Math. J. 26 pp 693– (1959)
[13] Wells, Am. Math. Monthly 83 pp 317– (1976)
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