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Proceedings of the American Mathematical Society

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ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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The $Q$-spectrum and spanning trees of tensor products of bipartite graphs
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by Timothy Y. Chow PDF
Proc. Amer. Math. Soc. 125 (1997), 3155-3161 Request permission

Abstract:

Recently, Knuth and Ciucu independently proved the surprising fact, conjectured by Stanley, that one connected component of the tensor product of a path with itself (the so-called “Aztec diamond graph”) has four times as many spanning trees as the other connected component, independent of the length of the path. We show here that much more is true: the connected components of the tensor product of any connected bipartite multigraphs all have essentially the same $Q$-spectrum. It follows at once that there is a simple formula relating their numbers of spanning trees.
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Additional Information
  • Timothy Y. Chow
  • Email: tchow@umich.edu
  • Received by editor(s): May 16, 1996
  • Additional Notes: The author was supported in part by an NSF postdoctoral fellowship.
  • Communicated by: Jeffry N. Kahn
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 3155-3161
  • MSC (1991): Primary 05C50, 05C05, 05C30; Secondary 15A18, 15A69
  • DOI: https://doi.org/10.1090/S0002-9939-97-04049-5
  • MathSciNet review: 1415578