If for each edge e of G there is a fractional [a, b]-factor with the indicator function h such that \(h(e) = 1,\) then G is called a fractional [a, b]-covered graph. A graph G is fractional (a, b, k)-critical covered if after deleting any k vertices of G, the remaining graph of G is fractional [a, b]-covered. The existence of a fractional (a, b, k)-critical covered graph plays an important role in transmitting data of networks. In this paper, we focus on the existence of a fractional (a, b, k)-critical covered graph from the spectral perspective. Specifically, we present a tight sufficient condition in terms of the spectral radius for a graph to be fractional (a, b, k)-critical covered, which extends nicely the result of Wang et al. (Linear Algebra Appl 666:1–10, 2023) from \(k=0\) to general k.
