On Domination in Matroids of Graphs
Jyoti D K1, Thukarama V2
1Jyoti D K, Department of Mathematics, Government College for Women, Mandya (Karnataka), India.
2Dr. Thukarama V, Department of Mathematics, Government First Grade College, Tipur (Karnataka), India.
Manuscript received on 11 July 2026 | First Revised Manuscript received on 25 July 2026 | Second Revised Manuscript received on 19 September 2026 | Manuscript Accepted on 15 October 2026 | Manuscript published on 30 October 2026 | PP: 10-12 | Volume-6 Issue-2, October 2026 | Retrieval Number: 100.1/ijam.B125106021026 | DOI: 10.54105/ijam.B1251.06021026
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© The Authors. Published by Lattice Science Publication (LSP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: The concept of domination has increasingly found powerful extensions within the structural framework of matroid theory. This paper investigates the structural, algebraic, and algorithmic properties of domination in matroids, unifying classical network domination with matroidal invariants such as closures, independent sets, and fundamental circuits. We formalise the notion of a dominating configuration in a general matroid M = (E, I) and analyse the combinatorial parameters governing its minimal representations. Specifically, we characterize the complexity of computing the minimum-weight domination number across prominent matroid classes, including graphic matroids. By leveraging the matroid rank function r(M), we establish novel lower and upper bounds for the domination invariant.
Keywords: Matroid Theory, Combinatorial Optimisation, Matroid Invariants, Graphic Matroids.
Scope of the Article: Number Theory