Γ-Extension of Binary Matroids

الملخص EN

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.