Spectral radius and spanning trees of graphs

2022/12/11 by Guoyan Ao, Ruifang Liu, Ao, Guoyan +3 · 1 citation
Mathematics · Computer Science · #Graph theory and applications #Advanced Graph Theory Research #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2212.05455

Abstract

For integer k≥2, a spanning k-ended-tree is a spanning tree with at most k leaves. Motivated by the closure theorem of Broersma and Tuinstra [Independence trees and Hamilton cycles, J. Graph Theory 29 (1998) 227--237], we provide tight spectral conditions to guarantee the existence of a spanning k-ended-tree in a connected graph of order n with extremal graphs being characterized. Moreover, by adopting Kaneko's theorem [Spanning trees with constraints on the leaf degree, Discrete Appl. Math. 115 (2001) 73--76], we also present tight spectral conditions for the existence of a spanning tree with leaf degree at most k in a connected graph of order n with extremal graphs being determined, where k≥1 is an integer.

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• Spanning k-trees, odd [1,b]-factors and spectral radius in binding graphs

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