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ISRN Discrete Mathematics
Volume 2011 (2011), Article ID 629707, 8 pages
http://dx.doi.org/10.5402/2011/629707
Research Article

Γ-Extension of Binary Matroids

Department of Mathematics, Faculty of Sciences, University of Urmia, P.O. Box 57135, Urmia, Iran

Received 13 August 2011; Accepted 22 September 2011

Academic Editors: Y. Hou and T. Prellberg

Copyright © 2011 Habib Azanchiler. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We extend the notion of a point-addition operation from graphs to binary matroids. This operation can be expressed in terms of element-addition operation and splitting operation. We consider a special case of this construction and study its properties. We call the resulting matroid of this special case a Γ-extension of the given matroid. We characterize circuits and bases of the resulting matroids and explore the effect of this operation on the connectivity of the matroids.