Minimizing algebraic connectivity over connected graphs with fixed girth

被引：33

作者：

Fallat, SM ^{[1
]}

Kirkland, S ^{[1
]}

Pati, S ^{[1
]}

机构：

[1] Univ Regina, Dept Math & Stat, Regina, SK S4S 0A2, Canada

来源：

DISCRETE MATHEMATICS | 2002年 / 254卷 / 1-3期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Laplacian matrix; algebraic connectivity; girth; unicyclic graph; Perron value; characteristic set;

D O I：

10.1016/S0012-365X(01)00355-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G,g denote the class of all connected graphs on n vertices with fixed girth g. We prove that if n greater than or equal to 3g-1, then the graph which uniquely minimizes the algebraic connectivity over G,g is the unicyclic "lollipop" graph C-n,C-g obtained by appending a g cycle to a pendant vertex of a path on n - g vertices. The characteristic set of C-n,C-g is also discussed. Throughout both algebraic and combinatorial techniques are used. (C) 2002 Elsevier Science B.V. All rights reserved.

引用

页码：115 / 142

页数：28

共 50 条

[21] Connectivity of graphs with given girth pair
Balbuena, C.
Cera, M.
Dianez, A.
Garcia-Vazquez, P.
Marcote, X.
DISCRETE MATHEMATICS, 2007, 307 (02) : 155 - 162
[22] On the connectivity of certain graphs of high girth
Lazebnik, F
Viglione, R
DISCRETE MATHEMATICS, 2004, 277 (1-3) : 309 - 319
[23] ALGEBRAIC CONNECTIVITY OF GRAPHS
FIEDLER, M
CZECHOSLOVAK MATHEMATICAL JOURNAL, 1973, 23 (02) : 298 - 305
[24] Maximizing Algebraic Connectivity in the Space of Graphs With a Fixed Number of Vertices and Edges
Ogiwara, Kohnosuke
Fukami, Tatsuya
Takahashi, Norikazu
IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS, 2017, 4 (02): : 359 - 368
[25] Coloring graphs with fixed genus and girth
Gimbel, J
Thomassen, C
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 349 (11) : 4555 - 4564
[26] Distributed Estimation and Control of Algebraic Connectivity Over Random Graphs
Di Lorenzo, Paolo
Barbarossa, Sergio
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2014, 62 (21) : 5615 - 5628
[27] On the homogeneous algebraic graphs of large girth and their applications
Shaska, T.
Ustimenko, V.
LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 430 (07) : 1826 - 1837
[28] On the restricted connectivity and superconnectivity in graphs with given girth
Balbuena, C.
Cera, M.
Dianez, A.
Garcia-Vazquez, P.
Marcote, X.
DISCRETE MATHEMATICS, 2007, 307 (06) : 659 - 667
[29] On connected signed graphs with rank equal to girth
Wu, Qi
Lu, Yong
Tam, Bit-Shun
LINEAR ALGEBRA AND ITS APPLICATIONS, 2022, 651 : 90 - 115
[30] Algebraic connectivity of directed graphs
Wu, CW
LINEAR & MULTILINEAR ALGEBRA, 2005, 53 (03): : 203 - 223

← 1 2 3 4 5 →