Bull. Korean Math. Soc. 2015; 52(3): 955-962
Printed May 31, 2015
https://doi.org/10.4134/BKMS.2015.52.3.955
Copyright © The Korean Mathematical Society.
Eunice Mphako-Banda
University of the Witwatersrand
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.
Keywords: Dowling group geometry, matroid, tree, characteristic poly\-nomial
MSC numbers: Primary 05B35, 05C31; Secondary 05C05, 05C07
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