Laplacian eigenvalue condition for a graph to have the strong parity property

\n A graph $G$ contains a strong parity factor $F$ if for every subset $X\\subseteq V(G)$ with $|X|$ even, $G$ has a spanning subgraph $F$ satisfying $\\delta(F)\\geq1$, $d_F(u)\\equiv1$ (mod 2) for any $u\\in X$, and $d_F(v)\\equiv0$ (mod 2) for any $v\\in V(G)\\setminus X$. Some scholars investigated the existence of strong parity factors in graphs and presented some results for graphs to have strong parity factors. In this paper, we proceed to study the existence of a strong parity factor in a graph and obtain a Laplacian eigenvalue condition to ensure that a graph has a strong parity factor.\n