For a finite group G let Gamma(G) denote the graph defined on the non-identity elements of G in such a way that two distinct vertices are connected by an edge if and only if they generate G. We look for conditions on the positive integer in that ensure that Gamma(G) contains a Hamiltonian cycle when G is the wreath product of a finite simple group S and a cyclic group of order m.
The generating graph of some monolithic groups
CRESTANI, ELEONORA;LUCCHINI, ANDREA
2012
Abstract
For a finite group G let Gamma(G) denote the graph defined on the non-identity elements of G in such a way that two distinct vertices are connected by an edge if and only if they generate G. We look for conditions on the positive integer in that ensure that Gamma(G) contains a Hamiltonian cycle when G is the wreath product of a finite simple group S and a cyclic group of order m.
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