Spectral radius and size conditions for fractional (a,b,l)-critical graphs

In recent years, research on the spectral extremal problems of fractional [a,b]-factors has attracted the attention of many scholars. The main content of our research is the generalization of fractional [a,b]-factors, namely fractional (a,b,l)-critical graph. Let a and b be two positive integers. A graph G is called a fractional (a,b,l)-critical graph if after deleting any l vertices of G the remaining graph of G has a fractional [a,b]-factor. In this paper, we present spectral radius and size conditions for a graph to be fractional (a,b,l)-critical.