A Sharp Upper Bound for the Number of Spanning Trees of a Graph

被引：0
|
作者：
Kinkar Ch. Das
机构：
[1] Université Paris-XI,
[2] Orsay,undefined
[3] LRI,undefined
来源：
Graphs and Combinatorics | 2007年 / 23卷
关键词：
Graph; spanning trees; Laplacian matrix;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let G = (V,E) be a simple graph with n vertices, e edges and d1 be the highest degree. Further let λi, i = 1,2,...,n be the non-increasing eigenvalues of the Laplacian matrix of the graph G. In this paper, we obtain the following result: For connected graph G, λ2 = λ3 = ... =  λn-1 if and only if G is a complete graph or a star graph or a (d1,d1) complete bipartite graph.
引用
下载
收藏
页码：625 / 632
页数：7
相关论文
共 50 条
  • [1] A sharp upper bound for the number of spanning trees of a graph
    Das, Kinkar Ch.
    GRAPHS AND COMBINATORICS, 2007, 23 (06) : 625 - 632
  • [2] UPPER BOUND FOR NUMBER OF SPANNING TREES OF A GRAPH
    GRIMMETT, GR
    DISCRETE MATHEMATICS, 1976, 16 (04) : 323 - 324
  • [3] SHARP UPPER BOUNDS FOR THE NUMBER OF SPANNING TREES OF A GRAPH
    Feng, Lihua
    Yu, Guihai
    Jiang, Zhengtao
    Ren, Lingzhi
    APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2008, 2 (02) : 255 - 259
  • [4] On the upper bound for the number of spanning trees of a connected graph
    Li, Rao
    Journal of Combinatorial Mathematics and Combinatorial Computing, 2015, 95 : 257 - 269
  • [5] A New Upper Bound on the Number of Spanning Trees of a Graph
    Li, Rao
    UTILITAS MATHEMATICA, 2013, 91 : 339 - 343
  • [6] A simple upper bound for the number of spanning trees of regular graphs
    Voblyi, V. A.
    DISCRETE MATHEMATICS AND APPLICATIONS, 2008, 18 (04): : 363 - 366
  • [7] A simple upper bound for the number of spanning trees of regular graphs
    Discrete Math Appl, 2008, 4 (363-366):
  • [8] The number of spanning trees of a graph
    Kinkar C Das
    Ahmet S Cevik
    Ismail N Cangul
    Journal of Inequalities and Applications, 2013
  • [9] The number of spanning trees of a graph
    Li, Jianxi
    Shiu, Wai Chee
    Chang, An
    APPLIED MATHEMATICS LETTERS, 2010, 23 (03) : 286 - 290
  • [10] The number of spanning trees of a graph
    Das, Kinkar C.
    Cevik, Ahmet S.
    Cangul, Ismail N.
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013,
12345