  In this paper we introduce a spectra preserving relation between graphs with
loops and graphs without loops. This relation is achieved in two steps. First,
by generalizing spectra results got on (m, k)-stars to a wider class of graphs,
the (m, k, s)-stars with or without loops. Second, by defining a covering space
of graphs with loops that allows to remove the presence of loops by increasing
the graph dimension. The equivalence of the two class of graphs allows to study
graph with loops as simple graph without loosing information.
