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Semigroups of mappings on graphs

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Abstract

At present, there are quite a few investigations in the theory of semigroups devoted to semigroups of mappings on graphs. Up to now, endomorphism semigroups of graphs, extensive transformation semigroups of graphs, coloring semigroups of graphs and other semigroups of special mappings on graphs have been studied. The results obtained show the way graphs are determined by the above-mentioned semigroups. They also show the structure of semigroups of mappings and interrelations between properties of graphs and corresponding properties of semigroups associated with the graphs. This paper gives a survey of the main results in this field.

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  1. Department of Mathematics, Saratov Pedagogical Institute, 410028, Saratov, USSR

    V. A. Molchanov

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Communicated by L.M. Gluskin and Boris M. Schein

Dedicated to Professor E.S. Lyapin on the occasion of his 70th birthday

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Molchanov, V.A. Semigroups of mappings on graphs. Semigroup Forum 27, 155–199 (1983). https://doi.org/10.1007/BF02572738

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