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arXiv · 2212.05455

Spectral radius and spanning trees of graphs

Guoyan Ao·Ruifang Liu·Jinjiang Yuan
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Abstract

For integer $k\geq2,$ 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 $k\geq1$ is an integer.

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Guoyan Ao, Ruifang Liu, Jinjiang Yuan. 2022-12-11. Spectral radius and spanning trees of graphs. https://arxiv.org/abs/2212.05455

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