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.
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页码：625 / 632
页数：7
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