Ali Ghalavand

activity

20232025

collaborators

4 papers

math.CO2025

On a Conjecture about Comparing the First and Second Zagreb Indices of Graphs

Ali Ghalavand

Let $G$ be a graph with order $n (G)$ , size $m (G)$ , first Zagreb index $M_{1} (G)$ , and second Zagreb index $M_{2} (G)$ . More than twenty years ago, it was conjectured that $\frac{M_1(G)}…

math.CO2025

On the local metric dimension of $K_{4}$ -free graphs

Ali Ghalavand, Sandi Klavžar, Xueliang Li

Let $G$ be a graph of order $n (G)$ , local metric dimension $dim_{l} (G)$ , and clique number $ω (G)$ . It has been conjectured that if $n (G) \geq ω (G) + 1 \geq 4$ , then $ \dim_l…

math.CO2024

Interplay between the local metric dimension and the clique number of a graph

Ali Ghalavand, Sandi Klavžar, Xueliang Li

The local metric dimension $dim_{l}$ in relation to the clique number $ω$ is investigated. It is proved that if $ω (G) \leq n (G) - 3$ , then $dim_{l} (G) \leq n (G) - 3$ and the gra…

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…

On a Conjecture about Comparing the First and Second Zagreb Indices of Graphs

On the local metric dimension of K4​-free graphs

Interplay between the local metric dimension and the clique number of a graph

Graphs whose mixed metric dimension is equal to their order

On the local metric dimension of $K_{4}$ -free graphs