论文标题
光谱半径和跨越图的树
Spectral radius and spanning trees of graphs
论文作者
论文摘要
对于整数$ k \ geq2，$ a跨度$ k $ -endend-tree是一棵树，最多可$ k $叶子。由Broersma和Tuinstra的封闭定理的激励[独立树和汉密尔顿周期，J。Graph Doemon 29（1998）29（1998）227--237]，我们提供了紧密的频谱条件，以保证存在具有极好图表的订单$ n $的跨度$ k $ - $ k $ -endene -tree的存在。此外，通过采用Kaneko的定理[跨越叶子学位的限制的树木，离散。数学。 115（2001）73--76]，我们还提出了一个紧密的频谱条件，以在连接的订单$ n $的连接图中具有叶子度最多具有叶子度的生成树，并确定$ k \ geq1 $是整数。
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.
