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

Let G=(V(G),E(G)) be a graph with vertex set V(G) and edge set E(G). A graph is ID-factor-critical if for every independent set I of G whose size has the same parity as |V(G)|, G−I has a perfect matching. For two positive integers a and b with a≤b, let h: E(G)→[0,1] be a function on E(G) satisfying a≤∑_e∈EG(vi)h(e)≤b for any vertex v_i∈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∈E(G)|h(e)>0} and E_G(v_i)={e∈E(G)|e is incident with v_i in G}. A graph is defined as a fractional [a,b]-deleted graph if for any e∈E(G), G−e contains a fractional [a,b]-factor. For any integer k≥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.