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

Win Min Aye; Tao Tian; Liming Xiong

doi:10.1016/j.amc.2019.03.062

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

Win Min Aye, Tao Tian, Liming Xiong^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

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)} (t _T (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 t _T (x) is the number of edge-disjoint paths with length at least two that start at a vertex x.

Original language	English
Pages (from-to)	258-262
Number of pages	5
Journal	Applied Mathematics and Computation
Volume	357
DOIs	https://doi.org/10.1016/j.amc.2019.03.062
Publication status	Published - 15 Sept 2019

Keywords

3-tree
Spanning tree
Square graph

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10.1016/j.amc.2019.03.062

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title = "Number of vertices of degree three in spanning 3-trees in square graphs",

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) (t T (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 t T (x) is the number of edge-disjoint paths with length at least two that start at a vertex x.",

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author = "Aye, {Win Min} and Tao Tian and Liming Xiong",

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AU - Aye, Win Min

AU - Tian, Tao

AU - Xiong, Liming

PY - 2019/9/15

Y1 - 2019/9/15

N2 - 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) (t T (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 t T (x) is the number of edge-disjoint paths with length at least two that start at a vertex x.

AB - 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) (t T (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 t T (x) is the number of edge-disjoint paths with length at least two that start at a vertex x.

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KW - Spanning tree

KW - Square graph

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VL - 357

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EP - 262

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

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

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Keywords

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