Characterizing path-factor deleted graphs via

A graph G has a P≥k-factor if G has a spanning subgraph H such that every component of H is a path of order at least k. A graph G is P≥k-factor deleted if G − e has a P≥k-factor for each edge e ∈ E(G). In this paper, we study the P≥2-factor deleted graphs by their Q-index (the largest eigenvalue of the signless Laplacian matrix) and D-index (the largest eigenvalue of the distance matrix). Sufficient conditions (in terms of Q-index and D-index) to guarantee that a graph G is a P≥2-factor deleted graph are established.