A graph \emph{G} is said to be \emph{determined by its spectrum} if any graph having the same spectrum as that of \emph{G} is isomorphic to \emph{G}. In this paper, it was proved that $K_{n}-E(lP_{2}) $ and $K_{n}-E(K_{1,l})$ are determined by their spectra, respectively.
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摘要: 只有与 G 同构的图才有相同的谱, 则称图 G 称为谱唯一确定的. 本文证明了, $K_{n}-E(lP_{2})$ 和 $K_{n}-E(K_{1,l})$ 是谱唯一确定的.
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关键词:
- O157.5
Abstract: A graph \emph{G} is said to be \emph{determined by its spectrum} if any graph having the same spectrum as that of \emph{G} is isomorphic to \emph{G}. In this paper, it was proved that $K_{n}-E(lP_{2}) $ and $K_{n}-E(K_{1,l})$ are determined by their spectra, respectively.-
Key words:
- cospectral graphs
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[1] {1}VAN DAM E R, HAEMERS W H. Which graph are determined by theirspectrum?[J]. Linear Algebra Appl, 2003, 373: 241-272.{2}WU T, HU S. Some edges-deleted subgraphs of complete graph aredetermined by their spectrum [J]. Journal of Mathematical Research\& Exposition, 2010, 30: 833-840.{3}CVETKOVI\'{C} D M, DOOB M, SACHS H. Spectra of graphs[M]. New York:John Wiley \& Son, 1980.{4}SHEN X, HOU Y, ZHANG Y. Graph $Z_{n}$ and some graphs related to$Z_{n}$ are determined by their spectrum[J]. Linear Algebra Appl,2005, 404: 58-68.
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