The Tutte polynomial of matroids constructed by a family of splitting operations

Document Type : Original paper

Authors

Urmia University

Abstract

To extract some more information from the constructions of matroids that arise from new operations, computing the Tutte polynomial, plays an important role. In this paper, we consider applying three operations of splitting, element splitting and splitting off to a binary matroid and then introduce the Tutte polynomial of resulting matroids by these operations in terms of that of original matroids.

Keywords

Main Subjects

References

[1] G. Azadi, Generalized splitting operation for binary matroids and related results, Ph.D. thesis, University of Pune, 2001.
[2] T. Brylawski and J. Oxley, The tutte polynomial and its applications, Matroid Applications (N. White, ed.), Cambridge University Press, Cambridge, 1992, pp. 123–225.
[3] H.H. Crapo, The Tutte polynomial, Aequationes Math. 3 (1969), no. 3, 211–229.
[4] J.G. Oxley, Matroid Theory, vol. 3, Oxford University Press, USA, 2006.
[5] T.T. Raghunathan, M.M. Shikare, and B.N. Waphare, Splitting in a binary matroid, Discrete Math. 184 (1998), no. 1-3, 267–271.
[6] M.M. Shikare and G. Azadi, Determination of the bases of a splitting matroid, European J. Combin. 24 (2003), no. 1, 45–52.
[7] M.M. Shikare, G. Azadi, and B.N. Waphare, Generalization of splitting off operation to binary matroids, Electron. Notes Discrete Math. 15 (2003), 186–188.
[8] M.M. Shikare, K.V. Dalvi, and S.B. Dhotre, Splitting off operation for binary matroids and its applications, Graphs Combin. 27 (2011), no. 6, 871–882.
 
Communications in Combinatorics and Optimization
Volume 7, Issue 1
June 2022
Pages 69-79

Files

Share

How to cite

Statistics