全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

一类单圈图的Laplacian谱刻画

DOI: 10.3969/j.issn.1006-7043.201107038

Keywords: Laplacian矩阵, Laplacian特征多项式, L?餐?谱, L?财?

Full-Text   Cite this paper   Add to My Lib

Abstract:

针对哪些图可由它们的谱刻画这一问题,在lollipop图和图??H(n;q,n1,n2)??的基础上定义了一类新的图类, 符号表示为??H(n;q,n1,n2,n3)??, 它是通过在圈??C??q的同一个顶点上连接3条悬挂路Pn1、Pn2Pn3而得到的顶点数为n??的单圈图. 首先, 证明了此图类中, 如果2个图形不同构, 那么它们必定具有不同的Laplacian谱. 在此结论的基础上, 证明了图??H(n;q,n1,n2,n3)??可由它的Laplacian谱刻画.

References

[1]  CVETKOVIC M, DOOB M, SACHS H. Spectra of graphs: theory and applications[M]. 3rd ed. Heidelberg-Leipzig: Johan Ambrosius Bart Verlag, 1995: 23-47.?
[2]  VAN DAM E R, HAEMERS W H. Which graphs are determined by their spectrum?[J]. Linear Algebra Appl, 2003, 373: 241-272.?
[3]  HAEMERS W H, LIU X G, ZHANG Y P. Spectral characterizations of lollipop graphs[J]. Linear Algebra Appl, 2008, 428: 2415-2423.?
[4]  LI J S, PAN Y L. A note on the second largest eigenvalue of the Laplacian matrix of a graph[J]. Linear and Multilinear Algebra, 2000, 48(20): 117-121.?
[5]  LIU X G, WANG S J, ZHANG Y P, et al. On the spectral characterization of some unicyclic graphs[J]. Discrete Mathematics, 2011, 311(21): 2317-2336.?
[6]  BRUALDI R A, CVETKOVIC D. A combinatorial approach to matrix theory and its applications[M]. Boca Raton: Chapman & Hall/CRC Press, 2009: 180.?
[7]  ?KELMANS A K, CHELNOKOV V M. A certain polynomial of a graph and graphs with an extremal number of trees[J]. Journal of Combinatorial Theory, Series B, 1974, 16: 197-214.?
[8]  LI J S, ZHANG X D. On the Laplacian eigenvalues of a graph[J]. Linear Algebra Appl, 1998, 285: 305-307.?
[9]  BIGGS N L. Algebraic graph theory[M]. 2nd ed. Cambridge: Cambridge University Press, 1993: 47-48.?
[10]  GUO J M. A conjecture on the algebraic connectivity of connected graphs with fixed girth[J]. Discrete Math, 2008, 308: 5702-5711.?
[11]  GUO J M. On the second largest Laplacian eigenvalue of trees[J]. Linear Algebra Appl, 2005, 404: 251-261.?

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133