The existence of even factors based on spectral conditions of graphs

Let $G=(V(G),E(G))$ be a graph with vertex set $V(G)$ and edge set $E(G)$. An even factor of $G$ is a spanning subgraph $F$ such that every vertex in $F$ has a nonzero even degree. Note that $\delta (G)\ge 2$ is a trivial necessary condition for a graph to have an even factor, where $\delta (G)$ is the minimum degree of $G$. In this paper, for a connected graph $G$ with minimum degree $\delta$, we establish a lower bound on the signless Laplacian spectral radius of $G$ and an upper bound on the distance spectral radius of $G$ such that $G$ contains an even factor.