M. Fazil

most citedLocating-Dominating Sets and Identifying Codes of a Graph Associated to a Finite Vector Space

4 citations · 6 across the 3 of their papers we have counts for

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math.CO2017

Locating-Dominating Sets of Functigraphs

Muhammad Murtaza, Muhammad Fazil, Imran Javaid +1

A locating-dominating set of a graph $G$ is a dominating set of $G$ such that every vertex of $G$ outside the dominating set is uniquely identified by its neighborhood within the d…

math.CO2017

On The Fixatic Number of Graphs

Muhammad Fazil, Imran Javaid

The fixing number of a graph $G$ is the smallest cardinality of a set of vertices $F \subseteq V (G)$ such that only the trivial automorphism of $G$ fixes every vertex in $F$ . Let $Π…

math.CO2017★ 4 cited

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…

math.CO2016

On the Distinguishing number of Functigraphs

Muhammad Fazil, Muhammad Mutaza, Usman Ali +1

Let $G_{1}$ and $G_{2}$ be disjoint copies of a graph $G$ , and let $g : V (G_{1}) \to V (G_{2})$ be a function. A functigraph $F_{G}$ consists of the vertex set $V(G_{1})\cup V(…

math.CO2016★ 2 cited

On Fixing number of Functigraphs

Muhammad Fazil, Imran Javaid, Muhammad Murtaza

The fixing number of a graph $G$ is the order of the smallest subset $S$ of its vertex set $V (G)$ such that stabilizer of $S$ in $G$ , $Γ_{S} (G)$ is trivial. Let $G_{1}$ and $G_{2}$ …