The Q-spectral radius and [a, b]-factors of graphs

Abstract

An [a, b]-factor of a graph G is a spanning subgraph H in which the degree of each vertex v satisfies a ≤ dH(v) ≤ b. In particular, when a = b = k, it is also called a k-factor. Let Q(G) and q(G) be the Q-matrix and the Q-spectral radius of G, respectively. Motivated by the conjecture of Cho, Hyun, O and Park [Bull. Korean Math. Soc. 58 (2021) 31–46] and the result of the spectral radius obtained by Fan, Lin and Lu [Discrete Math. 345 (2022) 112892], we in this paper consider the Q-spectral version of the above conjecture and present a tight sufficient condition in terms of the Q-spectral radius to guarantee the existence of [a, b]-factors in a graph.