M. Tavakoli

activity

20182023

most citedSome binary products and integer linear programming for computing

k

-metric dimension of graphs

2 citations · 2 across the 5 of their papers we have counts for

collaborators

Showing math.COShow all

8 papers · 1 filter

math.CO2023

Graphs whose mixed metric dimension is equal to their order

Ali Ghalavand, Sandi Klavžar, Mostafa Tavakoli

The mixed metric dimension $mdim (G)$ of a graph $G$ is the cardinality of a smallest set of vertices that (metrically) resolves each pair of elements from $V (G) \cup E (G)$ . We…

math.CO2022

On mixed metric dimension in subdivision, middle, and total graphs

Ali Ghalavand, Sandi Klavžar, Mostafa Tavakoli +1

Let $G$ be a graph and let $S (G)$ , $M (G)$ , and $T (G)$ be the subdivision, the middle, and the total graph of $G$ , respectively. Let $dim (G)$ , $edim (G)$ , and ${\rm mdim}…

math.CO2021

Global forcing number for maximal matchings in corona products

Sandi Klavžar, Mostafa Tavakoli, Gholamreza Abrishami

A global forcing set for maximal matchings of a graph $G = (V (G), E (G))$ is a set $S \subseteq E (G)$ such that $M_{1} \cap S \neq = M_{2} \cap S$ for each pair of maximal matchings $M_{1}$ an…

math.CO2021★ 2 cited

Some binary products and integer linear programming for computing $k$ -metric dimension of graphs

Sandi Klavžar, Freydoon Rahbarnia, Mostafa Tavakoli

Let $G$ be a connected graph. For an ordered set $S = {v_{1}, \dots, v_{ℓ}} \subseteq V (G)$ , the vector $r_{G} (v ∣ S) = (d_{G} (v_{1}, v), \dots, d_{G} (v_{ℓ}, v))$ is called the metric $S$ -repr…

math.CO2020

Edge metric dimensions via hierarchical product and integer linear programming

Sandi Klavžar, Mostafa Tavakoli

If $S = {v_{1}, \dots, v_{k}}$ is an ordered subset of vertices of a connected graph $G$ and $e$ is an edge of $G$ , then the vector $r_{G} (e ∣ S) = (d_{G} (v_{1}, e), \dots, d_{G} (v_{k}, e))$ is the…

math.CO2020

Dominated and dominator colorings over (edge) corona and hierarchical products

Sandi Klavžar, Mostafa Tavakoli

Dominator coloring of a graph is a proper (vertex) coloring with the property that every vertex is either alone in its color class or adjacent to all vertices of at least one color…

math.CO2019

Local metric dimension of graphs: generalized hierarchical products and some applications

Sandi Klavžar, Mostafa Tavakoli

Let $G$ be a graph and $S \subseteq V (G)$ . If every two adjacent vertices of $G$ have different metric $S$ -representations, then $S$ is a local metric generator for $G$ . A local met…

math.CO2018

Distribution of global defensive $k$ -alliances over some graph products

Mostafa Tavakoli, Sandi Klavžar

If $G = (V_{G}, E_{G})$ is a graph, then $S \subseteq V_{G}$ is a global defensive $k$ -alliance in $G$ if (i) each vertex not in $S$ has a neighbor in $S$ and (ii) each vertex of $S$ has at…

Graphs whose mixed metric dimension is equal to their order

On mixed metric dimension in subdivision, middle, and total graphs

Global forcing number for maximal matchings in corona products

Some binary products and integer linear programming for computing k-metric dimension of graphs

Edge metric dimensions via hierarchical product and integer linear programming

Dominated and dominator colorings over (edge) corona and hierarchical products

Local metric dimension of graphs: generalized hierarchical products and some applications

Distribution of global defensive k-alliances over some graph products

Some binary products and integer linear programming for computing $k$ -metric dimension of graphs

Distribution of global defensive $k$ -alliances over some graph products