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. In this paper it is shown that the graph Gamma(G) contains a Hamiltonian cycle for many finite groups G.
Hamiltonian cycles in the generating graphs of finite groups
LUCCHINI, ANDREA;
2010
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. In this paper it is shown that the graph Gamma(G) contains a Hamiltonian cycle for many finite groups G.
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