特征值互不相同的图(英文)On Graphs with Distinct Eigenvalues
马志辉,黄琼湘,张艳玲
摘要(Abstract)：
F.Harary和A.J.Schwenk[1]给出了一个开放性问题:什么样的图具有互不相同的特征值?到目前为止关于这方面的研究还很少.在本文中,将完全刻画了直径为d=n 2的连通二部图具有n个互不相同特征值的情况.最后,对直径为d=n 2的连通非二部图的情况给出了部分结果.
关键词(KeyWords)： 特征多项式;特征值;二部图;直径
基金项目(Foundation): Supported by NSFC Grant(No.10961023)
作者(Author): 马志辉,黄琼湘,张艳玲
参考文献(References)：
- [1]Harary F,Schwenk A J.Which graphs have integral spectra[M].Spring-Verlag,Berlin-Heidelberg-New York.1974,45-51.
- [2]Mowshowitz A.The group of a graph whose adjacency matrix has all distinct eigenvalues[J].Proof techniques in graph theory,New York;Academic press.1969,109-110.
- [3]Chao Chongyun.A note on the eigenvalues of a graph[J].Journal of combinatrial theory.1971,10:301-302.
- [4]Cvetkovic′D M,Doob M,Sachs H.Spectra of Graphs[M].Second edition,New York;JAcademic Press.1980.
- [5]Collatz L,Sinowinz U.Spekttren endlicher Gradfen[J].Abh Math Sem Univ Hamburg,1957,21:63-77.
- [6]Doob M,Haemers W H.The complement of the path is determined by its spectrum[J].Linear Algebra Appl,2002,356:57-65.
- [7]Schwenk A J.Computing the characteristic polynomial of a graph,Graphs and combinatioric[J].Lect Notes in Math,1973,406:275-307.
- [8]Godsil C,Royle G.Algebraic graph theory[M].Springer-verlag New York,Inc.2001.
- [9]Cvetkovic′D M,Rowlinson P,Simic′S.An Introduction to the Theory of Graph Spectra[M].Cambridge University Press-New York,2010.