The spanning k-trees, perfect matchings and spectral radius of graphs. Issue 21 (20th December 2022)

• Record Type: Journal Article
• Authors: Fan, Dandan; Goryainov, Sergey; Huang, Xueyi; Lin, Huiqiu
• Is Part Of: Linear & multilinear algebra. Volume 70:Issue 21(2022)
• Page Start: 7264
• Page End: 7275
• Publication Date: 2022-12-20
• Subjects: k-tree -- perfect matching -- spectral radius; 05C50; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2021.1985055
• Languages: English
• ISSNs: 0308-1087

Abstract

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.