Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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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.

$H$-trees, restrictions of Dowling group geometries

Eunice Mphako-Banda

University of the Witwatersrand

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.

Keywords: Dowling group geometry, matroid, tree, characteristic poly\-nomial

MSC numbers: Primary 05B35, 05C31; Secondary 05C05, 05C07