The spanning k-trees, perfect matchings and spectral radius of graphs. Issue 21 (20th December 2022) - Fan, Dandan; Goryainov, Sergey; Huang, Xueyi; Lin, Huiqiu
Abstract : A k -tree is a spanning tree in which every vertex has degree at most k . In this paper, we provide a sufficient condition for the existence of a k -tree in a connected graph with fixed order in terms of the adjacency spectral radius and the signless Laplacian spectral radius, respectively. Also, we give a similar condition for the existence of a perfect matching in a balanced bipartite graph with fixed order and minimum degree.