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A new graph product and its spectrum

  • C.D. Godsil (a1) and B.D. McKay (a2)
Abstract

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.

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References
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[1]Behzad, Mehdi, Chartrand, Gary, Introduction to the theory of graphs (Allyn and Bacon, Boston, 1971).
[2]Godsil, C. and McKay, B., “Some computational results on the spectra of graphs”, Combinatorial Mathematics IV, 7392 (Proc. Fourth Austral. Conf., University of Adelaide, 1975 Lecture Notes in Mathematics, 560. Springer-Verlag, Berlin, Heidelberg, New York, 1976).
[3]Sachs, Horst, “Beziehungen zwischen den in einem Graphen enthaltenen Kreisen und seinem charakteristischen Polynom”, Publ. Math. Debrecen 11 (1964), 119134.
[4]Schwenk, Allen J., “Computing the characteristic polynomial of a graph”, Graphs and combinatorics, 153172 (Proc. Capital Conf. Graph Theory and Combinatorics, George Washington University, 1973. Lecture Notes in Mathematics, 406. Springer-Verlag, Berlin, Heidelberg, New York, 1974).
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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