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Integral starlike trees

Published online by Cambridge University Press:  09 April 2009

Mamoru Watanabe  and
Allen J. Schwenk
Mamoru Watanabe
Affiliation:
Deoartment of Applied Mathematics Okayama College of ScienceOkayama 700, Japan
Allen J. Schwenk
Affiliation:
Department of Mathematics United States Naval Academy Annapolis Maryland 21402
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Abstract

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In this note we determine which of the trees homeomorphic to a star have a spectrum consisting entirely of integers. We also specify the integral double stars, and we consider the problem of trees with more complicated structure.

Subject classification (Amer. Math. Soc. (MOS) 1970): 05 C 05.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 1 , August 1979 , pp. 120 - 128
Copyright
Copyright © Australian Mathematical Society 1979

References

Collatz, L. and Sinogowitz, U. (1957), ‘Spectren endlicher Grafen’, Abh. Math. Sem. Univ. Hamburg 21, 63–77.Google Scholar
Graham, R. L. (1978), ‘On a diophantine equation arising in graph theory’, preprint, Bell Laboratories.Google Scholar
Harary, F. (1969), Graph theory (Addison-Wesley, Reading, Mass.).CrossRefGoogle Scholar
Harary, F., King, C., Mowshowitz, A. and Read, R. C. (1971), ‘Cospectral graphs and digraphs’, Bull. London Math. Soc. 3, 321–328.CrossRefGoogle Scholar
Harary, F. and Schwenk, A. J. (1974), ‘Which graphs have integral spectra?’, Graphs and Combinatorics, pp. 46–51 (Lecture Notes in Mathematics 406, Springer-Verlag, Berlin).Google Scholar
Sachs, H. (1964), ‘Beziehungen zwischen den in einem Graphen enthaltenen Kreisen und seinem characteristischen Polynom’ Publ. Math. (Debrecen) 11, 119–134.CrossRefGoogle Scholar
Schwenk, A. J. (1973), The spectrum of a graph (Ph.D. Thesis, University of Michigan).Google Scholar
Schwenk, A. J. (1974), ‘Computing the characteristic polynomial of a graph’ Graphs and Combinatorics, pp. 247–261 (Lecture Notes in Mathematics 406, Springer-Verlag, Berlin).Google Scholar
Schwenk, A. J. and Wilson, R. J. (1978), ‘On the eigenvalues of a graph’, Selected topics in graph theory, pp. 307–336 (Academic Press, London).Google Scholar