Γ-Extension of Binary Matroids. (3rd November 2011)

• Record Type: Journal Article
• Authors: Azanchiler Azanchiler, Habib Habib
• Other Names: Hou Hou Y. Y. Academic Editor.; Prellberg Prellberg T. T. Academic Editor.
• Is Part Of: ISRN discrete mathematics. Volume 2011(2011)
• Publication Date: 2011-11-03
• Subjects: Discrete mathematics -- Periodicals; Computer science -- Mathematics; Computer science -- Mathematics; Periodicals; 511.1
• DOI: 10.5402/2011/629707
• Languages: English
• ISSNs: 2090-7788

Abstract

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.