Commuting Regular Graphs for Non-commutative Semigroups

Authors

  • Azam Firuzkuhy Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran
  • Hossein Doostie Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran

DOI:

https://doi.org/10.26713/cma.v7i2.371

Keywords:

Commuting regular graphs, Commuting regular semigroups, Multi-graphs

Abstract

To study the commuting regularity of a semigroup, we use a graph. Indeed, we define a multi-graph for a semigroup and identify this graph for the semidirect product of two monogenic semigroups. For a non-group semigroup S, the ordered pair \((x, y)\) of the elements of \(S\) is called a commuting regular pair if for some \(z \in S\), \(xy = yxzyx\) holds, and \(S\) is called a commuting regular semigroup if every ordered pair of S is commuting regular. As a result of Abueida in 2013 concerning the heterogenous decomposition of uniform complete multi-graphs into the spanning edge-disjoint trees, we show that for a semigroup of order \(n\), the commuting regular graph of \(S\), \(\Gamma(S)\) has at most n spanning edge-disjoint trees.

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References

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Published

04-11-2016
CITATION

How to Cite

Firuzkuhy, A., & Doostie, H. (2016). Commuting Regular Graphs for Non-commutative Semigroups. Communications in Mathematics and Applications, 7(2), 115–119. https://doi.org/10.26713/cma.v7i2.371

Issue

Vol. 7 No. 2 (2016)

Section

Research Article

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