The Closure Operator, Flats and Hyperplanes of es-Splitting Matroid

Jump To References Section

Authors

  • P. P. Malavadkar
     ,IN
  • S. B. Dhotre
     ,IN
  • M. M. Shikare
     ,IN

DOI:

https://doi.org/10.18311/jims/2021/27838

Keywords:

Binary Matroid, es-splitting operation, closure operator, ats, hyperplanes
Primary, 05B35

Abstract

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.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Downloads

Published

2021-06-14

How to Cite

Malavadkar, P. P., Dhotre, S. B., & Shikare, M. M. (2021). The Closure Operator, Flats and Hyperplanes of es-Splitting Matroid. The Journal of the Indian Mathematical Society, 88(3-4), 334–345. https://doi.org/10.18311/jims/2021/27838

Issue

Volume 88, Issue 3-4, July-December 2021

Section

Articles

License

Copyright (c) 2021 P. P. Malavadkar, S. B. Dhotre, M. M. Shikare

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Crossref
Scopus
Google Scholar
Europe PMC
Received 2021-05-19
Accepted 2021-05-19
Published 2021-06-14

 

References

Habib Azanchiler, Extension of line-splitting operation from graphs to binary matroid, Lobachevskii J. Math., 24. (2006), 3-12.

Habib Azanchiler, A characterization of the bases of line-splitting matroids, Lobachevskii J. Math., 26. (2007), 5-15.

S. B. Dhotre, P. P. Malavadkar and M. M. Shikare, On 3-connected es-splitting binary matroids, Asian-European J. Math., 9. (1)(2016), 1650017-26.

S. Hedetniemi, Characterizations and constructions of minimally 2-connected graphs and minimally strong digraphs, Proceedings of the Second Louisiana Conference on Combinatorics, Graph Theory and Computing (1971), 257-282.

P. P. Malavadkar, M. M. Shikare and S. B. Dhotre, A characterization of n-connected splitting matroids, Asian-European J. Math., 7. (4)(2014), 1-7.

P. P. Malavadkar, M. M. Shikare and S. B. Dhotre, A characterization of cocircuits of an es-splitting matroid, J. Comb. Math. Comb. Comput., 105. (2018), 247-258.

P. P. Malavadkar, S. B. Dhotre and M. M. Shikare, Forbidden-minors for the class of cographic maroids which yield the graphic element splitting matroids, Southeast Asian Bull. Math., 43. (1)(2019), 105-119.

Oxley J. G., Matroid Theory, Oxford University Press, Oxford 1992.

T. T. Raghunathan, M. M. Shikare and B. N. Waphare, Splitting in a binary matroid, Discrete Mathematics, 184. (1998), 267-271.

M. M. Shikare, G. Azadi and B. N. Waphare, Generalized splitting operation for binary matroids and applications, J. Indian Math. Soc., 78. (1-4)(2011), 145-154.

M. M. Shikare, S. B. Dhotre and P. P. Malavadkar, A forbidden-minor characteriza- tion for the class of regular matroids which yield the cographic es-splitting matroids, Lobachevskii J. of Math., 34. (2013), 173-180.

P. J. Slater, A Classi cation of 4-connected graphs, J. Combin. Theory, 17. (1974), 282-298.

W. T. Tutte, Lectures on matroids, J. Res. Nat. Bur. Standards, B69. (1965), 1-47.

W. T. Tutte, A theory of 3-connected graphs, Indag. Math., 23. (1961), 441-455.

W. T. Tutte, Connectivity in matroids, Canad. J. Math., 18. (1966), 1301-1324.