On numbers of vertices of maximum degree in the spanning trees of a graph

被引：0
|
作者：
Fac. of Appl. Phys. and Mathematics, Gdańsk Technical University, Narutowicza 11/12, 80-952 Gdańsk, Poland [1 ]
不详 [2 ]
机构：
来源：
Discrete Math | / 1-3卷 / 247-258期
关键词：
D O I：
暂无
中图分类号：
学科分类号：
摘要：
For a connected graph G, let script T sign(G) be the set of all spanning trees of G and let nΔ(G) be the number of vertices of maximum degree in G. In this paper we show that if G is a cactus or a connected graph with p vertices and p+1 edges, then the set {nΔ(T) : T is a member of the set of script T sign(G)} has at most one gap, that is, it is a set of consecutive integers or it is the union of two sets each of which consists of consecutive integers.
引用
收藏
相关论文
共 50 条
  • [21] Degree Conditions for Graphs to Have Spanning Trees with Few Branch Vertices and Leaves
    Maezawa, Shun-ichi
    Matsubara, Ryota
    Matsuda, Haruhide
    [J]. GRAPHS AND COMBINATORICS, 2019, 35 (01) : 231 - 238
  • [22] Number of vertices of degree three in spanning 3-trees in square graphs
    Aye, Win Min
    Tian, Tao
    Xiong, Liming
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2019, 357 : 258 - 262
  • [23] Spanning Trees with a Bounded Number of Branch Vertices in a Claw-Free Graph
    Haruhide Matsuda
    Kenta Ozeki
    Tomoki Yamashita
    [J]. Graphs and Combinatorics, 2014, 30 : 429 - 437
  • [24] Spanning Trees with a Bounded Number of Branch Vertices in a Claw-Free Graph
    Matsuda, Haruhide
    Ozeki, Kenta
    Yamashita, Tomoki
    [J]. GRAPHS AND COMBINATORICS, 2014, 30 (02) : 429 - 437
  • [25] The Ramsey Numbers for Trees of Large Maximum Degree Versus the Wheel Graph W8
    Chng, Zhi Yee
    Britz, Thomas
    Tan, Ta Sheng
    Wong, Kok Bin
    [J]. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2024, 47 (04)
  • [26] DECOMPOSITION OF A GRAPH REALIZING A DEGREE SEQUENCE INTO DISJOINT SPANNING TREES
    KLEITMAN, DJ
    WANG, DL
    [J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 1976, 30 (02) : 206 - 221
  • [27] The Maximum Number of Spanning Trees of a Graph with Given Matching Number
    Muhuo Liu
    Guangliang Zhang
    Kinkar Chandra Das
    [J]. Bulletin of the Malaysian Mathematical Sciences Society, 2021, 44 : 3725 - 3732
  • [28] Spanning Trees of Bounded Degree, Connectivity, Toughness, and the Spectrum of a Graph
    Cunxiang Duan
    Ligong Wang
    [J]. Bulletin of the Iranian Mathematical Society, 2021, 47 : 185 - 196
  • [29] The number and degree distribution of spanning trees in the Tower of Hanoi graph
    Zhang, Zhongzhi
    Wu, Shunqi
    Li, Mingyun
    Comellas, Francesc
    [J]. THEORETICAL COMPUTER SCIENCE, 2016, 609 : 443 - 455
  • [30] Spanning Trees of Bounded Degree, Connectivity, Toughness, and the Spectrum of a Graph
    Duan, Cunxiang
    Wang, Ligong
    [J]. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2021, 47 (01) : 185 - 196
12345