On Graphs With a Given
نویسندگان
چکیده
On Graphs With A Given Endomorphism Monoid Benjamin Shemmer Hedrĺın and Pultr proved that for any monoid M there exists a graph G with endomorphism monoid isomorphic to M. We will give a construction G(M) for a graph with prescribed endomorphism monoid M. Using this construction we derive bounds on the minimum number of vertices and edges required to produce a graph with a given endomorphism monoid for various classes of finite monoids. We state bounds for the class of all monoids as well as for certain subclasses – groups, k-cancellative monoids, commutative 3-nilpotent monoids, rectangular groups, completely simple monoids, a variety of strong semillatices and others. On Graphs With a Given Endomorphism Monoid
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