2 citations · 4 across the 8 of their papers we have counts for
10 papers
Matroids with bases as minimal resolving sets of graphs
Usman Ali, Iffat Fida Hussain
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 mi…
An independence system as knot invariant
Usman Ali, Iffat Fida Hussain
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…
On the Distinguishing number of Functigraphs
Muhammad Fazil, Muhammad Mutaza, Usman Ali +1
Let and be disjoint copies of a graph , and let be a function. A functigraph consists of the vertex set $V(G_{1})\cup V(…
Power Graph and Exchange Property for Resolving Sets
Usman Ali, Ghulam Abbas, Syed Ahtisham Bokhary
A formula for computing the metric dimension of a simple graph, having no singleton twin, is given. A sufficient condition for a simple graph to have the exchange property, for res…
On Resolvability of a Graph Associated to a Finite Vector Space
Usman Ali, Syed Ahtisham Bokhary, Khola Wahid
The metric dimension of non-component graph, associated to a finite vector space, is determined. It is proved that the exchange property holds for resolving sets of the graph, exce…
On some automorphism related parameters in graphs
Imran Javaid, Hira Benish, Usman Ali +1
In this paper, we deduce some properties of -sets of connected graphs. Also, we introduce the concept of fixing share of each vertex of a fixing set to see the participation…