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Which graphs have integral spectra?

Part I: Invited Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 406)

Abstract

The spectrum S(G) of a graph G of order p is defined as the non-increasing sequence of the p real eigenvalues of the adjacency matrix of G. It has been found that certain graphs have an integral spectrum, i.e., every eigenvalue is an integer. Thus, it is natural to ask just which graphs have this property. We develop a systematic approach to this question based on operations on graphs. The general problem appears intractable.

Research supported in part by grant 73-2502 from the Air Force Office of Scientific Research.

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References

  1. Collatz, L., and Sinogowitz, U., Spektren endlicher Graphen, Abh. Math. Sem. Univ. Hamburg, 21 (1957) 64–77.

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© 1974 Springer-Verlag Berlin

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Harary, F., Schwenk, A.J. (1974). Which graphs have integral spectra?. In: Bari, R.A., Harary, F. (eds) Graphs and Combinatorics. Lecture Notes in Mathematics, vol 406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066434

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  • DOI: https://doi.org/10.1007/BFb0066434

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06854-9

  • Online ISBN: 978-3-540-37809-9

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