#### Alladi Ramakrishnan Hall

#### Automorphism group of Cayley graphs generated by transpositions

#### Ashwin Ganesan

##### Vidyalankar Institute of Technology, Mumbai

*I shall present some recent results on the automorphism group*

of some families of Cayley graphs. Let H be a group and let S be a

generating set for H. The automorphism group of every Cayley graph

Cay(H,S) contains the following two subgroups: the right regular

representation R(H) and the set Aut(H,S) of automorphisms of H that

fixes S setwise. A Cayley graph Cay(H,S) is said to be normal if it has

the smallest possible (full) automorphism group in the sense that it has

no other automorphisms besides R(H) Aut(H,S). An open problem in the

literature is to determine, given H and S, the normality and

automorphism group of Cay(H,S). We obtain some sufficient conditions

for a Cayley graph of the symmetric group generated by transpositions to

be normal. The automorphism group of the star graphs, bubble-sort

graphs and modified bubble-sort graphs are special cases of our result.

We also investigate the edge-transitivity and isomorphism classes of

Cayley graphs generated by transpositions.

Done