  More than 40 years ago Chv\'atal introduced a new graph invariant, which he
called graph toughness. From then on a lot of research has been conducted,
mainly related to the relationship between toughness conditions and the
existence of cyclic structures, in particular, determining whether the graph is
Hamiltonian and pancyclic. A pancyclic graph is certainly Hamiltonian, but not
conversely. Bondy in 1976, however, suggested the "metaconjecture" that almost
any nontrivial condition on a graph which implies that the graph is Hamiltonian
also implies that the graph is pancyclic. We confirm the Bondy conjecture for
t-tough graphs in the case when $t\in \{ 1;2;3\}$ in terms of the edge number,
the spectral radius and the signless Laplacian spectral radius of the graph.
