On the Finite Groups that all Their Semi-Cayley Graphs are Quasi-Abelian

Document Type : Communication

Author

University of Larestan, Larestan, I. R. Iran

Abstract

In this paper, we prove that every semi-Cayley graph over a group G is quasi-abelian if and only if G is abelian.

Keywords

Main Subjects

1. ‎M‎. ‎Arezoomand‎, ‎On the automorphism group of quasi-abelian semi-Cayley‎ graphs‎, Quasigroups and Related Systems‎, ‎submitted‎.

2. ‎M‎. ‎Arezoomand‎, ‎B‎. ‎Taeri‎, ‎On the characteristic polynomial of n-Cayley‎ digraphs‎, ‎Electron‎. ‎J‎. ‎Combin. 20 (3) (2013) #P‎. ‎57‎.

3. ‎M‎. ‎Arezoomand‎, ‎B‎. ‎Taeri‎, ‎Normality of 2-Cayley digraphs‎, ‎Discrete Math. 338 (2015) 41-47‎.

4. ‎X‎. ‎Gao‎, ‎Y‎. ‎Luo‎, ‎The spectrum of semi-Cayley graphs over abelian groups‎, Linear Algebra Appl. 432 (2010) 2974-2983.

5. ‎R‎. ‎Golstone‎, ‎K‎. ‎Weld‎, ‎Graphically abelian groups‎, ‎Discrete Math. 310 (2010) 2806-2810‎.

6. ‎M‎. ‎J‎. ‎de Resmini‎, ‎D‎. ‎Jungnickel‎, ‎Strongly regular semi-Cayley graphs‎, ‎J‎. Algebraic Combin. 1 (1992) 217-228.

7. ‎G‎. ‎Sabidussi‎. ‎Vertex-transitive graphs‎. ‎Monatsh‎. ‎Math. 68 (1964) 426-438.

8. ‎J‎. ‎Wang‎, ‎M.-Y‎. ‎Xu‎, ‎A class of Hamiltonian Cayley graphs and Parsons‎ graphs‎, ‎European J‎. ‎Combin. 18 (1997) 597-600‎.

9. ‎B‎. ‎Zgrablić, ‎Note on quasiabelian Cayley graphs‎, ‎Discrete Math. 226 (2001)‎ 445-447‎.

10. ‎B‎. ‎Zgrablić‎, ‎On quasiabelian Cayley graphs and graphical doubly regular representations‎, ‎Discrete Math. 244 (2002) 495-519.

11. ‎J‎. ‎X‎. ‎Zhou‎, ‎Y‎. ‎Q‎. ‎Feng‎, ‎Cubic bi-Cayley graphs over abelian groups‎, ‎European J‎. ‎Combin. 36 (2014) 679-693.

12. ‎J‎. ‎X‎. ‎Zhou‎, ‎Every finite group has a normal bi-Cayley graph‎, ‎Ars Math‎. Contemp. 14 (2018) 177-186‎.