TY - JOUR AU - Sorouhesh, Mohammad Reza AU - Doostie, Hossein AU - Campbell, Colin M. PY - 2017 TI - A sufficient condition for coinciding the Green graphs of semigroups JO - Journal of Mathematics and Computer Science SP - 216-219 VL - 17 IS - 2 AB - A necessary condition for coinciding the Green graphs \(\Gamma_{\textit{L}}(S), \Gamma_{\Re}(S), \Gamma_{\jmath}(S), \Gamma_{D}(S)\) and \(\Gamma_{H}(S)\) of a finite semigroup S has been studied by Gharibkhajeh [A. Gharibkhajeh, H. Dosstie, Bull. Iranian Math. Soc., 40 (2014), 413–421]. Gharibkhajeh et al. proved that the coinciding of Green graphs of a finite semigroup S implies the regularity of S. However, the converse is not true because of certain well-known examples of finite regular semigroups. We look for a sufficient condition on non-group semigroups that implies the coinciding of the Green graphs. Indeed, in this paper we prove that for every non-group quasi-commutative finite semigroup, all of the Green graphs are isomorphic. SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.017.02.03 DO - 10.22436/jmcs.017.02.03 ID - Sorouhesh2017 ER - TY - JOUR TI - Conjugacy classes and finite p-groups AU - E. Adan-Bante JO - Arch. Math. (Basel) PY - 2005 DA - 2005// VL - 85 ID - Adan-Bante2005 ER - TY - JOUR TI - Quasi-commutative semigroups and \(\sigma\)-reflexive semigroups AU - A. Cherubini AU - A. Varisco JO - Semigroup Forum PY - 1980 DA - 1980// VL - 19 ID - Cherubini1980 ER - TY - BOOK TI - The algebraic theory of semigroups I AU - A. H. Clifford AU - G. B. Preston PB - Amer. Math. Soc., Providence PY - 1961 DA - 1961// CY - ID - Clifford1961 ER - TY - JOUR TI - A graphical difference between the inverse and regular semigroups AU - A. Gharibkhajeh AU - H. Dosstie JO - Bull. Iranian Math. Soc. PY - 2014 DA - 2014// VL - 40 ID - Gharibkhajeh2014 ER - TY - BOOK TI - Special classes of Semigroups AU - A. Nagy PB - Kluwer Academic Publishers, Dordrecht PY - 2001 DA - 2001// CY - ID - Nagy2001 ER - TY - JOUR TI - Quasi-commutative semigroups I AU - N. P. Mukherjee JO - Czechoslovak Math. J. PY - 1972 DA - 1972// VL - 22 ID - Mukherjee1972 ER - TY - JOUR TI - Quasi-commutative semigroups of finite order related to Hamiltonian groups AU - M. R. Sorouhesh AU - H. Dosstie JO - Bull. Korean Math. Soc. PY - 2015 DA - 2015// VL - 52 ID - Sorouhesh2015 ER -