# Automorphism Groups of Some Graphs Related to Cycle Graph

## Authors

Arti Salat
Shri Govind Guru University, Godhra, Gujarat
Amit Sharma
Shri Govind Guru University, Godhra, Gujarat

### Synopsis

This paper deals with the automorphism groups of some graphs related to cycle Cn. In this paper, we derived the automorphism groups of some graphs related to cycle graph. Some cycle related graphs like the graph $$G = C(n, m)$$ obtained from two cycles Cn and Cm by joining their single vertices with an edge, the graph S(Cm1,Cm2,...,Cmn), the graph obtained from cycle Cn by attaching m1,m2,...,mn pendant edges to vertices v1,v2,...,vn, respectively of cycle Cn, the graph $$C_k(n^{l_1}_1, n^{l_2}_2, ..., n^{l_k}_k)$$, the graph obtained from the duplication of every edge of cycle by a new vertex, the graph obtained from the one point union of n−cycles of different lengths and the graph Ck (Cm1,Cm2,...,Cmk) have been elaborated successfully. The different theorems on automorphism groups have been proposed in some context of graphs related to cycle graph and obtained results have been justified with the help of examples.

Published
October 10, 2022