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Let $G=(V(G), E(G))$ be a graph with vertex set $V(G)$ and edge set $E(G)$. Agraph is $ID$-factor-critical if for every independent set $I$ of $G$ whosesize has the same parity as $|V(G)|$, $G-I$ has a perfect matching. For twopositive integers $a$ and $b$ with $a\leq b$, let $h$: $E(G)\rightarrow [0, 1]$be a function on $E(G)$ satisfying $a\leq\sum _{e\in E_{G}(v_{i})}h(e)\leq b$for any vertex $v_{i}\in V(G)$. Then the spanning subgraph with edge set$E_{h}$, denoted by $G[E_{h}]$, is called a fractional $[a, b]$-factor of $G$with indicator function $h$, where $E_{h}=\{e\in E(G)\mid h(e)>0\}$ and$E_{G}(v_{i})=\{e\in E(G)\mid e$ is incident with $v_{i}$ in $G$\}. A graph isdefined as a fractional $[a, b]$-deleted graph if for any $e\in E(G)$, $G-e$contains a fractional $[a, b]$-factor. For any integer $k\geq 1$, a graph has a$k$-factor if it contains a $k$-regular spanning subgraph. In this paper, wefirstly give a distance spectral radius condition of $G$ to guarantee that $G$is $ID$-factor-critical. Furthermore, we provide sufficient conditions in termsof distance spectral radius and distance signless Laplacian spectral radius fora graph to contain a fractional $[a, b]$-factor, fractional $[a,b]$-deleted-factor and $k$-factor.

Distance spectral conditions for $ID$-factor-critical and fractional $[a, b]$-factor of graphs