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

Let $G=\left(V\right(G),E(G\left)\right)$ be a graph with vertex set $V\left(G\right)$ and edge set $E\left(G\right)$. A graph is ID-factor-critical if for every independent set I of G whose size has the same parity as $\left|V\right(G\left)\right|$, $G-I$ has a perfect matching. For two positive integers a and b with $a\le b$, let h: $E\left(G\right)\to [0,1]$ be a function on $E\left(G\right)$ satisfying $a\le {\sum }_{e\in E_G\left(v_i\right)}h\left(e\right)\le b$ for any vertex $v_i\in V\left(G\right)$. Then the spanning subgraph with edge set $E_h$, denoted by $G\left[E_h\right]$, is called a fractional $[a,b]$-factor of G with indicator function h, where $E_h=\{e\in E(G\left)\right|h\left(e\right)>0\}$ and $E_G\left(v_i\right)=\{e\in E(G\left)\right|e$ is incident with $v_i$ in G}. A graph is defined as a fractional $[a,b]$-deleted graph if for any $e\in E\left(G\right)$, $G-e$ contains a fractional $[a,b]$-factor. For any integer $k\ge 1$, a graph has a k-factor if it contains a k-regular spanning subgraph. In this paper, we firstly give a distance spectral radius condition of G to guarantee that G is ID-factor-critical. Furthermore, we provide sufficient conditions in terms of distance spectral radius and distance signless Laplacian spectral radius for a graph to contain a fractional $[a,b]$-factor, fractional $[a,b]$-deleted-factor and k-factor.