Nima Ghanbari

activity

20142026

most citedSombor Index of Polymers

11 citations · 27 across the 34 of their papers we have counts for

collaborators

36 papers

math.CO2026

Super Coalition Number in Graphs

Saeid Alikhani, Nima Ghanbari

We introduce and investigate the structural properties of super coalition partitions in graphs, a novel direction that bridges cooperative resource deployment with rigid domination…

math.CO2026

Stability of the Strong Domination Number of Graphs

Saeid Alikhani, Nima Ghanbari, Mazharuddin Mehraban +1

This paper introduces and studies the stability of the strong domination number of a graph, denoted $st_{γ_{s t}} (G)$ , defined as the minimum number of vertices whose…

math.HO2024

Golden ratio in graph theory: A survey

Saeid Alikhani, Nima Ghanbari

Much has been written about the golden ratio $ϕ = \frac{1 + 5}{2}$ and this strange number appears mysteriously in many mathematical calculations. In this article, we review the…

math.CO2024

Counting the Number of Domatic Partition of a Graph

Saeid Alikhani, Davood Bakhshesh, Nima Ghanbari

A subset of vertices $S$ of a graph $G$ is a dominating set if every vertex in $V ∖ S$ has at least one neighbor in $S$ . A domatic partition is a partition of the vertices…

math.CO2024

Elliptic Sombor energy of a graph

Saeid Alikhani, Nima Ghanbari, Mohammad Ali Dehghanizadeh

Let $G$ be a simple graph with vertex set $V (G) = {v_{1}, v_{2}, \dots, v_{n}}$ . The elliptic Sombor matrix of $G$ , denoted by $A_{E S O} (G)$ , is defined as the $n \times n$ matrix whose…

math.CO2024

Strong coalitions in graphs

Hamidreza Golmohammadi, Saeid Alikhani, Nima Ghanbari +2

For a graph $G = (V, E)$ , a set $D \subset V (G)$ is a strong dominating set of $G$ , if for every vertex $x \in V (G) ∖ D$ there is a vertex $y \in D$ with $x y \in E (G)$ and $deg(x…

math.CO2023

Strong domination number of graphs from primary subgraphs

Saeid Alikhani, Nima Ghanbari, Michael A. Henning

A set $D$ of vertices is a strong dominating set in a graph $G$ , if for every vertex $x \in V (G) ∖ D$ there is a vertex $y \in D$ with $x y \in E (G)$ and $d e g (x) \leq d e g (y)$ .…

math.CO2023

Strong domatic number of a graph

Nima Ghanbari, Saeid Alikhani

A set $D$ of vertices of a simple graph $G = (V, E)$ is a strong dominating set, if for every vertex $x \in D = V ∖ D$ there is a vertex $y \in D$ with $x y \in E (G)$ and…

math.CO2023

Computational complexity aspects of super domination

Csilla Bujtás, Nima Ghanbari, Sandi Klavžar

Let $G$ be a graph. A dominating set $D \subseteq V (G)$ is a super dominating set if for every vertex $x \in V (G) ∖ D$ there exists $y \in D$ such that $N_G(y)\cap (V(G)\setmi…

math.CO2023

Strong domination number of Hajós sum and vertex-sum of two graphs

Nima Ghanbari, Saeid Alikhani

Let $G = (V, E)$ be a simple graph. A set $D \subseteq V$ is a strong dominating set of $G$ , if for every vertex $x \in V ∖ D$ there is a vertex $y \in D$ with $x y \in E (G)$ and $d…

math.CO2022

Strong domination number of a modified graph

Saeid Alikhani, Nima Ghanbari

Let $G = (V, E)$ be a simple graph. A set $D \subseteq V$ is a strong dominating set of $G$ , if for every vertex $x \in V ∖ D$ there is a vertex $y \in D$ with $x y \in E (G)$ and $d…

math.CO2022★ 1 cited

Super Domination: Graph Classes, Products and Enumeration

Nima Ghanbari, Gerold Jäger, Tuomo Lehtilä

The dominating set problem (DSP) is one of the most famous problems in combinatorial optimization. It is defined as follows. For a given simple graph $G = (V, E)$ , a dominating set of…

math.CO2022

Strong domination number of some operations on a graph

Saeid Alikhani, Nima Ghanbari, Hassan Zaherifar

Let $G = (V (G), E (G))$ be a simple graph. A set $D \subseteq V (G)$ is a strong dominating set of $G$ , if for every vertex $x \in V (G) ∖ D$ there is a vertex $y \in D$ with $xy\in…

math.CO2022

End Super Dominating Sets in Graphs

Saieed Akbari, Nima Ghanbari, Michael A. Henning

Let $G = (V, E)$ be a simple graph. A dominating set of $G$ is a subset $S \subseteq V$ such that every vertex not in $S$ is adjacent to at least one vertex in $S$ . The cardinality of…

math.CO2022

Sombor-index-like invariants of some graphs

Nima Ghanbari, Saeid Alikhani

The Sombor index (SO) is a vertex-degree-based graph invariant, defined as the sum over all pairs of adjacent vertices of $d_{i}^{2} + d_{j}^{2}$ , where $d_{i}$ is the degree of the $i$ …

math.CO2022★ 1 cited

Some results on the super domination number of a graph II

Nima Ghanbari

Let $G = (V, E)$ be a simple graph. A dominating set of $G$ is a subset $S \subseteq V$ such that every vertex not in $S$ is adjacent to at least one vertex in $S$ . The cardinality of…

math.CO2022

Some results on the super domination number of a graph

Nima Ghanbari

Let $G = (V, E)$ be a simple graph. A dominating set of $G$ is a subset $S \subseteq V$ such that every vertex not in $S$ is adjacent to at least one vertex in $S$ . The cardinality of…

math.CO2021

Co-even domination number of some binary operations on graphs

Nima Ghanbari

Let $G = (V, E)$ be a simple graph. A dominating set of $G$ is a subset $D \subseteq V$ such that every vertex not in $D$ is adjacent to at least one vertex in $D$ . The cardinality of…

math.CO2021

More on co-even domination number

Nima Ghanbari

Let $G = (V, E)$ be a simple graph. A dominating set of $G$ is a subset $D \subseteq V$ such that every vertex not in $D$ is adjacent to at least one vertex in $D$ . The cardinality of…

math.CO2021

Co-even Domination Number of a Modified Graph by Operations on a Vertex or an Edge

Nima Ghanbari, Saeid Alikhani, Mohammad Ali Dehghanizadeh

Let $G = (V, E)$ be a simple graph. A dominating set of $G$ is a subset $D \subseteq V$ such that every vertex not in $D$ is adjacent to at least one vertex in $D$ . The cardinality of…

math.CO2021

Secure domination number of $k$ -subdivision of graphs

Nima Ghanbari

Let $G = (V, E)$ be a simple graph. A dominating set of $G$ is a subset $D \subseteq V$ such that every vertex not in $D$ is adjacent to at least one vertex in $D$ . The cardinality of…

math.CO2021

On the Graovac-Ghorbani and atom-bond connectivity indices of graphs from primary subgraphs

Nima Ghanbari

Let $G = (V, E)$ be a finite simple graph. The Graovac-Ghorbani index of a graph G is defined as $ABC_{GG}(G)=\sum_{uv\in E(G)}\sqrt{\frac{n_u(uv,G)+n_v(uv,G)-2}{n_u(uv,G)n_v(uv,G)}},…

math.CO2021

On the Sombor characteristic polynomial and Sombor energy of a graph

Nima Ghanbari

Let $G$ be a simple graph with vertex set $V (G) = {v_{1}, v_{2}, \dots, v_{n}}$ . The Sombor matrix of $G$ , denoted by $A_{S O} (G)$ , is defined as the $n \times n$ matrix whose $(i, j)$ -en…

math.CO2021

Mostar index and edge Mostar index of polymers

Nima Ghanbari, Saeid Alikhani

Let $G = (V, E)$ be a graph and $e = uv \in E$ . Define $n_{u} (e, G)$ be the number of vertices of $G$ closer to $u$ than to $v$ . The number $n_{v} (e, G)$ can be defined in an analogous way. Th…

Super Coalition Number in Graphs

Stability of the Strong Domination Number of Graphs

Golden ratio in graph theory: A survey

Counting the Number of Domatic Partition of a Graph

Elliptic Sombor energy of a graph

Strong coalitions in graphs

Strong domination number of graphs from primary subgraphs

Strong domatic number of a graph

Computational complexity aspects of super domination

Strong domination number of Hajós sum and vertex-sum of two graphs

Strong domination number of a modified graph

Super Domination: Graph Classes, Products and Enumeration

Strong domination number of some operations on a graph

End Super Dominating Sets in Graphs

Sombor-index-like invariants of some graphs

Some results on the super domination number of a graph II

Some results on the super domination number of a graph

Co-even domination number of some binary operations on graphs

More on co-even domination number

Co-even Domination Number of a Modified Graph by Operations on a Vertex or an Edge

Secure domination number of k-subdivision of graphs

On the Graovac-Ghorbani and atom-bond connectivity indices of graphs from primary subgraphs

On the Sombor characteristic polynomial and Sombor energy of a graph

Mostar index and edge Mostar index of polymers

Secure domination number of $k$ -subdivision of graphs