Number of vertices of degree three in spanning 3-trees in square graphs

Win Min Aye, Tao Tian and Liming Xiong

Applied Mathematics and Computation, 2019, vol. 357, issue C, 258-262

Abstract: In this paper, we show that the square graph of a tree T has a spanning tree of maximum degree at most three and with at most max{0,∑x∈W≥3(T)(tT(x)−2)−2} vertices of degree three, where W≥3(T)={x∈V(T): there are at least three edge-disjoint paths of length at least two that start x} and tT(x) is the number of edge-disjoint paths with length at least two that start at a vertex x.

Keywords: Square graph; 3-tree; Spanning tree (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:357:y:2019:i:c:p:258-262

DOI: 10.1016/j.amc.2019.03.062

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