A graph G has a strong parity factor if for every subset \(X\subseteq V(G)\) with |X| even, G has a spanning subgraph F with minimum degree at least one such that \(d_F(v)\equiv 1\) \((\text {mod}~2)\) for all \(v\in X\) , and \(d_F(u)\equiv 0\) \((\text {mod}~2)\) for all \(u\in V(G)-X\) . In this paper, we give a sufficient spectral condition for the existence of a strong parity factor in a connected graph with minimum degree \(\delta\) , and an upper bound for the third largest eigenvalue in a connected r-regular graph to have a strong parity factor.
