The existence of even factors based on the $A_{\alpha }$-spectral radius of graphs

Abstract

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 $A_{\alpha }$-spectral radius of $G$ such that $G$ contains an even factor.