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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

MSC:
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C99 Graph theory
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