A spectral condition for a graph having a strong parity factor

Abstract: 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 $v\in V(G)\setminus X$. In this paper, we give a spectral radius condition to guarantee that a connected graph contains a strong parity factor.