arXiv subjects

Iffat Fida Hussain

Publications and source records attributed to Iffat Fida Hussain.

2 recordsLinked to original sources

arXiv2024

Matroids with bases as minimal resolving sets of graphs

We define an independence system associated with simple graphs. We prove that the independence system is a matroid for certain families of graphs, including trees, with bases as minimal resolving sets. Consequently, the greedy algorithm on the matroid can be used to find the minimum-cost resolving set of weighted graphs, wherein the independent system is a matroid. We also characterize hyperplanes of the matroid for trees and prove that its dual matroid is loop-free.

math.CO↗

arXiv2019

An independence system as knot invariant

In this article, we define an independence system for a classical knot diagram and prove that the independence system is a knot invariant for alternating knots. We also discuss the exchange property for minimal unknotting sets. Finally, we show that there are knot diagrams where the independence system is a matroid and there are knot diagrams where it is not.

math.GT↗