caa a22 4500 605461767 CHVBK 20210128100245.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10114-015-4356-8 doi (NATIONALLICENCE)springer-10.1007/s10114-015-4356-8 Isomorphisms of finite semi-Cayley graphs [Elektronische Daten] [Majid Arezoomand, Bijan Taeri] Let G be a finite group. A Cayley graph over G is a simple graph whose automorphism group has a regular subgroup isomorphic to G. A Cayley graph is called a CI-graph (Cayley isomorphism) if its isomorphic images are induced by automorphisms of G. A well-known result of Babai states that a Cayley graph Γ of G is a CI-graph if and only if all regular subgroups of Aut(Γ) isomorphic to G are conjugate in Aut(Γ). A semi-Cayley graph (also called bi-Cayley graph by some authors) over G is a simple graph whose automorphism group has a semiregular subgroup isomorphic to G with two orbits (of equal size). In this paper, we introduce the concept of SCI-graph (semi-Cayley isomorphism) and prove a Babai type theorem for semi-Cayley graphs. We prove that every semi-Cayley graph of a finite group G is an SCI-graph if and only if G is cyclic of order 3. Also, we study the isomorphism problem of a special class of semi-Cayley graphs. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Semi-Cayley graph nationallicence Cayley graph nationallicence CI-graph nationallicence semiregular subgroup nationallicence Arezoomand Majid Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111, Isfahan, Iran aut Taeri Bijan Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111, Isfahan, Iran aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/4(2015-04-01), 715-730 1439-8516 31:4<715 2015 31 10114 https://doi.org/10.1007/s10114-015-4356-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-4356-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Arezoomand Majid Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111, Isfahan, Iran aut NATIONALLICENCE 700 1- Taeri Bijan Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111, Isfahan, Iran aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/4(2015-04-01), 715-730 1439-8516 31:4<715 2015 31 10114