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Shikare, M. M.
- Generalized Splitting Operation for Binary Matroids and its Applications
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Authors
Affiliations
1 Department of Mathematics, University of Pune, Pune - 411 007, IN
2 Department of Mathematics, University of Urmia, Urmia 57135-165, IR
1 Department of Mathematics, University of Pune, Pune - 411 007, IN
2 Department of Mathematics, University of Urmia, Urmia 57135-165, IR
Source
The Journal of the Indian Mathematical Society, Vol 78, No 1-4 (2011), Pagination: 145-154Abstract
In this paper, we introduce the notion of generalized split- ting operation for binary matroids as an extension of the corresponding operation for graphs. The circuits and the bases of the new matroid are characterized. Under the reverse operation, we determine those binary matroids, each of which yields a given matroid by applying the splitting operation on them.Keywords
Graph, Binary Matroid, Circuit, Minor, Splitting Operation.
- The Closure Operator, Flats and Hyperplanes of es-Splitting Matroid
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Authors
Affiliations
1 Dr. Vishwanath Karad MIT World Peace University, School of Mathematics and Statistics, Pune, IN
2 Savitribai Phule Pune University, Department of Mathematics, Pune, IN
1 Dr. Vishwanath Karad MIT World Peace University, School of Mathematics and Statistics, Pune, IN
2 Savitribai Phule Pune University, Department of Mathematics, Pune, IN
Source
The Journal of the Indian Mathematical Society, Vol 88, No 3-4 (2021), Pagination: 334–345Abstract
The es-splitting operation on binary matroids is a natural generalization of Slater's n-line splitting operation on graphs. In this paper, we characterize the closure operator of the es-splitting binary matroid MeX in terms of the closure operator of the original binary matroid M. We also describe the ats and the hyperplanes of the es-splitting bi- nary matroid MeX in terms of the ats and the hyperplanes, respectively of the original binary matroid M.Keywords
Binary Matroid, es-splitting operation, closure operator, ats, hyperplanesReferences
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