On cyclic graphs of finite semigroups. (English) Zbl 1306.20059
Summary: We define and study the cyclic graph \(\Gamma_S\) of a finite semigroup \(S\). We obtain some graph theoretical properties of \(\Gamma_S\) including its dominating number, independence number and genus of the graph. Then, we study the cyclic graphs \(\Gamma_{\mathbb Z_n}\) and \(\Gamma_{\mathrm{GL}_n(F)}\), where \(\mathbb Z_n\) is the semigroup under multiplicative operation and \(\mathrm{GL}_n(F)\) is the set of all \(n\times n\) invertible matrices over a finite field \(F\) with multiplicative operation.
MSC:
| 20M10 | General structure theory for semigroups |
| 05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
| 05C10 | Planar graphs; geometric and topological aspects of graph theory |
| 05C69 | Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) |
Keywords:
cyclic graphs; finite semigroups; idempotents; dominating numbers; independence numbers; genusReferences:
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