Unretractive and S-unretractive joins and lexicographic products of graphs

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 this property if and only if the second f...

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Bibliographic Details
Published in:Journal of graph theory 1987-09, Vol.11 (3), p.429-440
Main Author: Knauer, Ulrich
Format: Article
Language:English
Subjects:
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Mathematics
Sciences and techniques of general use
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Summary: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 this 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 endomorphisms.
ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.3190110316