# Extension of Line-splitting Operation from Graphs to Binary Matroid

## (*Lobachevskii Journal of Mathematics, Volume XXIV*)

In this paper, we characterize the *n*-line splitting
operation of graphs in terms of cycles of respective graphs and then
extend this operation to binary matroids.
In matroids, we call this operation an element-set splitting. The
resulting matroid is called the es-splitting matroid. We
characterize circuits of an es-splitting matroid. We also characterize
the es-splitting matroid in terms of matrices. Also, we show
that if *M* is a connected binary matroid then the es-splitting
matroid *M* ^{e}_{X}
is also connected.