2 research outputs found
Spectral radius and spanning trees of graphs
For integer a spanning -ended-tree is a spanning tree with at
most 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
-ended-tree in a connected graph of order 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 in a connected graph of order with extremal
graphs being determined, where is an integer