Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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H-TREES, RESTRICTIONS OF DOWLING GROUP GEOMETRIES

  • Mphako-Banda, Eunice (The John Knopfmacher Centre for Applicable Analysis and Number Theory School of Mathematics University of the Witwatersrand)
  • Received : 2014.06.10
  • Published : 2015.05.31
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Abstract

It has been established that the role played by complete graphs in graph theory is similar to the role Dowling group geometries and Projective geometries play in matroid theory. In this paper, we introduce a notion of H-tree, a class of representable matroids which play a similar role to trees in graph theory. Then we give some properties of H-trees such that when q = 0, then the results reduce to the known properties of trees in graph theory. Finally we give explicit expressions of the characteristic polynomials of H-trees, H-cycles, H-fans and H-wheels.

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References

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