LAPLACIAN COEFFICIENTS OF UNICYCLIC GRAPHS WITH THE NUMBER OF LEAVES AND GIRTH

被引：3

作者：

Zhang, Jie ^{[1
,2
,3
,4
]}

Zhang, Xiao-Dong ^{[1
,2
]}

机构：

[1] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

[2] Shanghai Jiao Tong Univ, MOE LSC, Shanghai 200240, Peoples R China

[3] Shanghai Finance Univ, Sch Insurance, Shanghai 201209, Peoples R China

[4] Shanghai Finance Univ, GuoGou Free Trade Zone Financial Res Inst, Shanghai 201209, Peoples R China

来源：

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS | 2014年 / 8卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Unicyclic graph; Laplacian coefficients; Laplacian-like energy; balanced starlike tree; WIENER INDEX; TREES; ENERGY;

D O I：

10.2298/AADM140715008Z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Motivated by Ilic and Ilic's conjecture [A. ILIC, M. ILIC: Laplacian coefficients of trees with given number of leaves or vertices of degree two. Linear Algebra Appl., 431 (2009), 2195-2202.], we investigate properties of the minimal elements in the partial set (U-n,l(g),<=) of the Laplacian coefficients, where U-n,l(g) denote the set of n-vertex unicyclic graphs with the number of leaves l and girth g. These results are used to disprove their conjecture. Moreover, the graphs with minimum Laplacian-like energy in U-n,l(g) are also studied.

引用

页码：330 / 345

页数：16

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