In paper [1] F.Harary and Schwenk give an open problem: Which graphs have distinct eigenvalues? Unfortunately
there have been few results on the question.In this paper
we will characterize the connected bipartite graphs that has n distinct eigenvalues with diameter d = n 2 and give some results about the graphs which are non-bipartite with d = n 2 in the end.
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references
Harary F,Schwenk A J.Which graphs have integral spectra[M].Spring-Verlag,Berlin-Heidelberg-New York.1974,45-51.
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.
Chao Chongyun.A note on the eigenvalues of a graph[J].Journal of combinatrial theory.1971,10:301-302.
Cvetkovic′D M,Doob M,Sachs H.Spectra of Graphs[M].Second edition,New York;JAcademic Press.1980.
Collatz L,Sinowinz U.Spekttren endlicher Gradfen[J].Abh Math Sem Univ Hamburg,1957,21:63-77.
Doob M,Haemers W H.The complement of the path is determined by its spectrum[J].Linear Algebra Appl,2002,356:57-65.
Schwenk A J.Computing the characteristic polynomial of a graph,Graphs and combinatioric[J].Lect Notes in Math,1973,406:275-307.
Godsil C,Royle G.Algebraic graph theory[M].Springer-verlag New York,Inc.2001.
Cvetkovic′D M,Rowlinson P,Simic′S.An Introduction to the Theory of Graph Spectra[M].Cambridge University Press-New York,2010.