Abstract: In this paper, we will generate the wreath product
11 12 M wrM using only two permutations. Also, we will show the
structure of some groups containing the wreath product 11 12 M wrM .
The structure of the groups founded is determined in terms of wreath
product k (M wrM ) wrC 11 12 . Some related cases are also included.
Also, we will show that 132K+1 S and 132K+1 A can be generated
using the wreath product k (M wrM ) wrC 11 12 and a transposition in
132K+1 S and an element of order 3 in 132K+1 A . We will also show
that 132K+1 S and 132K+1 A can be generated using the wreath
product 11 12 M wrM and an element of order k +1.
Abstract: The length of a cycle basis of a graph is the sum of the lengths of its elements. A minimum cycle basis is a cycle basis with minimum length. In this work, a construction of a minimum cycle basis for the wreath product of wheels with stars is presented. Moreover, the length of minimum cycle basis and the length of its longest cycle are calculated.