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.
Highlights
Habib AzanchilerWe extend the notion of a point-addition operation from graphs to binary matroids
Slater 1 defined few operations for graphs which preserve connectedness of graphs. One such operation is a point-addition vertex-addition operation. This operation is defined in the following way
Let H be the graph obtained from G by adding a new vertex v adjacent to vertices v1, v2, . . . , vn of G
Summary
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
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