On the Cayley graphs of symmetric group S_۴

Let S_n be the symmetric group of degree n. In this paper, we classify non-isomorphic Cayley graphs of S_۴ of valency ۳. Moreover, we verify that there are exactly ۱۰ non-isomorphic  Cayley graphs of S_۴ with valency ۳. Also, we classify  the valency ۳ CI-graphs of    Cayley graphs of  S_۴ and  we prove that S_۴ is not a CI-group and does not possess the ۳-CI-property. We show that  there are at least ۱۰ non-isomorphic Cayley graphs of the symmetric group S_n with valency ۳.

کلیدواژه ها:

Cayley graph ، Symmetric group ، Isomorphism