4 citations · 16 across the 7 of their papers we have counts for
9 papers
Distinguishing Number of Non-Zero Component Graphs
I. Javaid, M. Murtaza, H. Benish
A non-zero component graph associated to a finite vector space is a graph whose vertices are non-zero vectors of and two vertices are adja…
The Fractional Local Metric Dimension of Graphs
Hira Benish, Muhammad Murtaza, Imran Javaid
The fractional versions of graph theoretic-invariants multiply the range of applications in scheduling, assignment and operational research problems. In this paper, we introduce th…
Automorphism related parameters of a graph associated to a finite vector space
Hira Benish, Imran Javaid, M. Murtaza
In this paper, we discuss automorphism related parameters of a graph associated to a finite vector space. The fixing neighborhood of a pair of vertices of a graph is th…
Locating-Dominating Sets of Functigraphs
Muhammad Murtaza, Muhammad Fazil, Imran Javaid +1
A locating-dominating set of a graph is a dominating set of such that every vertex of outside the dominating set is uniquely identified by its neighborhood within the d…
Locating-Dominating Sets and Identifying Codes of a Graph Associated to a Finite Vector Space
Muhammad Murtaza, Imran Javaid, Muhammad Fazil
In this paper, we investigate the problem of covering the vertices of a graph associated to a finite vector space as introduced by Das \cite{Das}, such that we can uniquely identif…
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(…
On Fixing number of Functigraphs
Muhammad Fazil, Imran Javaid, Muhammad Murtaza
The fixing number of a graph is the order of the smallest subset of its vertex set such that stabilizer of in , is trivial. Let and …
On The Fixed Number of Graphs
I. Javaid, M. Murtaza, M. Asif +1
An automorphism on a graph is a bijective mapping on the vertex set , which preserves the relation of adjacency between any two vertices of . An automorphism fixes…
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…