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Article type: Research Article
Authors: Wu, Qiuxin
Affiliations: College of Science, Beijing Information Science and Technology University, Beijing 100196, China. E-mail: qxwu@263.net
Abstract: A 3-tree is a tree with the maximum degree at most three. Let T be a tree of order n and p(T). In this paper, we prove that the square of T has a spanning tree F in which every leave of T has degree one or two and F has at most max{min{⌊n−p(T)+72⌋,⌊n−12⌋},2} leaves; This implies that the square graph of a connected graph G has the same conclusion above as a tree. These bounds are all sharp in same sense. We also give a shorter proof of a result in [10].
Keywords: Square graph, 3-tree, spanning tree, factor
DOI: 10.3233/JCM-160598
Journal: Journal of Computational Methods in Sciences and Engineering, vol. 16, no. 1, pp. 21-27, 2016
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