Distance spectral conditions for (a,b,k)-critical graphs

The study of characterizing the existence of [ a , b ] -factors based on eigenvalue conditions can be traced back to the work of Brouwer and Haemers (2005) on perfect matchings. In recent years, many scholars have focused on the spectral extremal problems of [ a , b ] -factors. Our research focuses on ( a , b , k ) -critical graphs, which are a natural generalization of [ a , b ] -factors. A graph G is called an ( a , b , k ) -critical graph if after deleting any k vertices of G the remaining graph of G has an [ a , b ] -factor. In this paper, by using technical structure theorems and typical spectral methods, we provide a distance spectral radius condition for a graph to be ( a , b , k ) -critical. As a corollary, we also obtain a distance spectral radius condition for a graph to have an [ a , b ] -factor.