The spread of unicyclic graphs with given size of maximum matchings

被引：17

作者：

Li, Xueliang ^{[1
]}

Zhang, Jianbin

Zhou, Bo

机构：

[1] Nankai Univ, Ctr Cominator, Tianjin 300071, Peoples R China

[2] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

[3] S China Normal Univ, Dept Math, Guangzhou 510631, Peoples R China

来源：

JOURNAL OF MATHEMATICAL CHEMISTRY | 2007年 / 42卷 / 04期

关键词：

spread; unicyclic graph; characteristic polynomial; eigenvalue;

D O I：

10.1007/s10910-006-9141-6

中图分类号：

O6 [化学];

学科分类号：

0703 ;

摘要：

The spread s(G) of a graph G is defined as s(G) = max (i,j) |lambda (i) -lambda (j)|, where the maximum is taken over all pairs of eigenvalues of G. Let U(n,k) denote the set of all unicyclic graphs on n vertices with a maximum matching of cardinality k, and U*(n,k) the set of triangle-free graphs in U(n,k). In this paper, we determine the graphs with the largest and second largest spectral radius in U*(n,k), and the graph with the largest spread in U(n,k).

引用

页码：775 / 788

页数：14

共 14 条

[1]

[Anonymous], PUBL I MATH BEOGRAD

[2]

[Anonymous], MATCH COMMUN COMPUT

[3] On the spectral radius of unicyclic graphs with perfect matchings [J].

Chang, A ;

Tian, F .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2003, 370 :237-250

[4]

CVETKOIC D, 1997, EIGENSPACES GRAPHS

[5] A TABLE OF CONNECTED GRAPHS ON 6 VERTICES [J].

CVETKOVIC, D ;

PETRIC, M .

DISCRETE MATHEMATICS, 1984, 50 (01) :37-49

[6] SPECTRA OF UNICYCLIC GRAPHS [J].

CVETKOVIC, D ;

ROWLINSON, P .

GRAPHS AND COMBINATORICS, 1987, 3 (01) :7-23

[7]

CVETKOVIC D, 1980, SEPCTRA GRAPHS THEOR

[8] The spread of the spectrum of a graph [J].

Gregory, DA ;

Hershkowitz, D ;

Kirkland, SJ .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 332 :23-35

[9]

GUO JM, 2001, LINEAR ALGEBRA APPL, V329, P1

[10] Bounds on the largest eigenvalues of trees with a given size of matching [J].

Hou, YP ;

Li, JS .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 342 (1-3) :203-217

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