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

Author

Listed:
  • Aye, Win Min
  • Tian, Tao
  • Xiong, Liming

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.

Suggested Citation

  • Aye, Win Min & Tian, Tao & Xiong, Liming, 2019. "Number of vertices of degree three in spanning 3-trees in square graphs," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 258-262.
    • Handle: RePEc:eee:apmaco:v:357:y:2019:i:c:p:258-262
    DOI: 10.1016/j.amc.2019.03.062
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