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A new graph product and its spectrum

Published online by Cambridge University Press:  17 April 2009

C.D. Godsil  and
B.D. McKay
C.D. Godsil
Affiliation:
Department of Mathematics, Syracuse University, Syracuse, New York, USA;
B.D. McKay
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria.
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Abstract

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A new graph product is introduced, and the characteristic polynomial of a graph so–formed is given as a function of the characteristic polynomials of the factor graphs. A class of trees produced using this product is shown to be characterized by spectral properties.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 18 , Issue 1 , February 1978 , pp. 21 - 28
Copyright
Copyright © Australian Mathematical Society 1978

References

[1]Behzad, Mehdi, Chartrand, Gary, Introduction to the theory of graphs (Allyn and Bacon, Boston, 1971).Google Scholar
[2]Godsil, C. and McKay, B., “Some computational results on the spectra of graphs”, Combinatorial Mathematics IV, 73–92 (Proc. Fourth Austral. Conf., University of Adelaide, 1975 Lecture Notes in Mathematics, 560. Springer-Verlag, Berlin, Heidelberg, New York, 1976).CrossRefGoogle Scholar
[3]Sachs, Horst, “Beziehungen zwischen den in einem Graphen enthaltenen Kreisen und seinem charakteristischen Polynom”, Publ. Math. Debrecen 11 (1964), 119–134.CrossRefGoogle Scholar
[4]Schwenk, Allen J., “Computing the characteristic polynomial of a graph”, Graphs and combinatorics, 153–172 (Proc. Capital Conf. Graph Theory and Combinatorics, George Washington University, 1973. Lecture Notes in Mathematics, 406. Springer-Verlag, Berlin, Heidelberg, New York, 1974).CrossRefGoogle Scholar