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Graphs and ranks of monoids
Authors:Behnam Khosravi
Institution:Department of Mathematics, Institute for Advanced Studies in Basic Sciences, Zanjan, Iran
Abstract:For a finite monoid S, let ν(S) (νd(S)) denote the least number n such that there exists a graph (directed graph) Γ of order n with End(Γ)?S. Also let rank(S) be the smallest number of elements required to generate S. In this paper, we use Cayley digraphs of monoids, to connect lower bounds of ν(S) (νd(S)) to the lower bounds of rank(S). On the other hand, we connect upper bounds of rank(S) to upper bounds of ν(S) (νd(S)).
Keywords:Cayley digraphs of monoids  endomorphism monoids of graphs
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