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

被引：2
|
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
收藏
页码：330 / 345
页数：16
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