On the Laplacian coefficients of bicyclic graphs

被引：30

作者：

He, Chang-Xiang ^{[1
]}

Shan, Hai-Ying ^{[2
]}

机构：

[1] Shanghai Univ Sci & Technol, Coll Sci, Shanghai 200093, Peoples R China

[2] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

来源：

DISCRETE MATHEMATICS | 2010年 / 310卷 / 23期

基金：

中国国家自然科学基金;

关键词：

Bicyclic graph; Characteristic polynomial; Laplacian coefficients; TREES;

D O I：

10.1016/j.disc.2010.08.012

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a graph of order n and let P(G, x) = Sigma(n)(k=0)(-1)(k)c(k)x(n-k) be the characteristic polynomial of its Laplacian matrix. Generalizing the approach in [D. Stevanovic, A. Ilic, On the Laplacian coefficients of unicyclic graphs, Linear Algebra and its Applications 430 (2009) 2290-2300.] on graph transformations, we show that among all bicyclic graphs of order n, the kth coefficient c(k) is smallest when the graph is B-n (obtained from C-4 by adding one edge connecting two non-adjacent vertices and adding n 4 pendent vertices attached to the vertex of degree 3). (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：3404 / 3412

页数：9

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