A. Ghalavand

activity

20192025

most citedOn a Conjecture about Degree Deviation Measure of Graphs

2 citations · 2 across the 17 of their papers we have counts for

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19 papers · 1 filter

math.CO2025

On Neutral Edge Sets in Anti-Ramsey Numbers

Ali Ghalavand, Qing Jie, Zemin Jin +2

The anti-Ramsey number of a graph $G$ , introduced by Erdős et al.\ in 1975, is the maximum number of colors in an edge-coloring of the complete graph $K_{n}$ that avoids a rainbow co…

math.CO2025

On the Anti-Ramsey Number Under Edge Deletion

Ali Ghalavand, Qing Jie, Zemin Jin +2

According to a study by Erdős et al. in 1975, the anti-Ramsey number of a graph $G$, denoted as $AR(n, G)$, is defined as the maximum number of colors that can be used in an ed…

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

Anti-Ramsey Numbers for Spanning Linear Forests of 3-Vertex Paths and Matchings

Ali Ghalavand, Xueliang Li

A subgraph in an edge-colored graph is called rainbow if all its edges have distinct colors. For a graph $G$ and an integer $n$ , the anti-Ramsey number $A R (n, G)$ is the maximum num…

math.CO2025

Intertwining local (adjacency) metric dimension with the clique number of a graph

Ali Ghalavand, Sandi Klavžar, Xueliang Li

Let $G$ be a simple connected graph with order $n (G)$ , local metric dimension $dim_{l} (G)$ , local adjacency metric dimension $dim_{A, l} (G)$ , and clique number $ω (G)$ ,…

math.CO2025

On the local metric dimension of $K_{5}$ -free graphs

Ali Ghalavand, Xueliang Li

Let $ G $ be a graph with order $ n(G) \geq 5 $, local metric dimension $ \dim_l(G) $, and clique number $ ω(G) $. In this paper, we investigate the local metric dimension…

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.CO2025

On decycling and forest numbers of Cartesian products of trees

Ali Ghalavand, Sandi Klavžar, Ning Yang

The decycling number $\nabla (G)$ of a graph $G$ is the minimum number of vertices that must be removed to eliminate all cycles in $G$ . The forest number $f (G)$ is the maximum numbe…

math.CO2025

On Maximum Induced Forests of the Balanced Bipartite Graphs

Ali Ghalavand, Xueliang Li

The decycling number $\nabla (G)$ of a graph $G$ is the minimum number of vertices that must be removed to eliminate all cycles in $G$ . The forest number $f (G)$ is the maximum numbe…

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…

math.CO2022

Graph Irregularity Characterization with Particular Regard to Bidegreed Graphs

Ali Ghalavand, Tamás Réti, Igor Z. Milovanović +1

In this study we are interested mainly in investigating the relations between two graph irregularity measures which are widely used for structural irregularity characterization of…

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

On the Number of $k -$ Matchings in Graphs

Kinkar Ch. Das, Ali Ghalavand, Ali Reza Ashrafi

Suppose $G$ is a undirected simple graph. A $k -$ subset of edges in $G$ without common vertices is called a $k -$ matching and the number of such subsets is denoted by $p (G, k)$ . The a…

math.CO2021

Laplacian Coefficients of a Forest in terms of the Number of Closed Walks in the Forest and its Line Graph

Ali Ghalavand, Ali Reza Ashrafi

Let $G$ be a finite simple graph with Laplacian polynomial $ψ (G, λ) = \sum_{k = 0}^{n} (- 1)^{n - k} c_{k} λ^{k}$ . In an earlier paper, the coefficients $c_{n - 4}$ and $c_{n - 5}$ for tree with respec…

math.CO2021

On a Conjecture About the Sombor Index of Graphs

Kinkar Chandra Das, Ali Ghalavand, Ali Reza Ashrafi

Let $G$ be a graph with vertex set $V (G)$ and edge set $E (G)$ . The Sombor and reduced Sombor indices of $G$ are defined as $S O (G) = \sum_{uv \in E (G)} d e g_{G} (u)^{2} + d e g_{G} (v)^{2}$ and…

math.CO2020★ 2 cited

On a Conjecture about Degree Deviation Measure of Graphs

Ali Ghalavand, Ali Reza Ashrafi

Let G be an n-vertex graph with m edges. The degree deviation measure of G is defined as s(G)=sum v in V(G)|degG(v)-(2m/n)|, where n and m are the number of vertices and edges of G…

math.CO2019

Maximum Zagreb Indices Among All p-Quasi k-Cyclic Graphs

A Ghalavand, A R Ashrafi

A simple connected graph G is called a p-quasi k-cyclic graph, if there exists a subset S of vertices such that |S|=p, G-S is k-cyclic and there is no a subset S` of V(G) such that…

math.CO2019

First and Second Maximum of Randić Index Among all $k -$ Cyclic Graphs of a Given Order

Ali Reza Ashrafi, Ali Ghalavand, Marzieh Pourbabaee

Suppose $G$ is a simple graph with edge set $E (G)$ . The Randić index $R (G)$ is defined as $R (G) = \sum_{uv \in E (G)} \frac{1}{d e g _{G} ( u ) d e g _{G} ( v )}$ , where $d e g_{G} (u)$ denotes th…

On Neutral Edge Sets in Anti-Ramsey Numbers

On the Anti-Ramsey Number Under Edge Deletion

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

Anti-Ramsey Numbers for Spanning Linear Forests of 3-Vertex Paths and Matchings

Intertwining local (adjacency) metric dimension with the clique number of a graph

On the local metric dimension of K5​-free graphs

On the local metric dimension of K4​-free graphs

On decycling and forest numbers of Cartesian products of trees

On Maximum Induced Forests of the Balanced Bipartite Graphs

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

Graphs whose mixed metric dimension is equal to their order

Graph Irregularity Characterization with Particular Regard to Bidegreed Graphs

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

On the Number of k−Matchings in Graphs

Laplacian Coefficients of a Forest in terms of the Number of Closed Walks in the Forest and its Line Graph

On a Conjecture About the Sombor Index of Graphs

On a Conjecture about Degree Deviation Measure of Graphs

Maximum Zagreb Indices Among All p-Quasi k-Cyclic Graphs

First and Second Maximum of Randić Index Among all k−Cyclic Graphs of a Given Order

On the local metric dimension of $K_{5}$ -free graphs

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

On the Number of $k -$ Matchings in Graphs

First and Second Maximum of Randić Index Among all $k -$ Cyclic Graphs of a Given Order