Nima Ghanbari
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Nima Ghanbari has a total of 13 co-authors. Here are the top co-authors by number of shared publications:
- Saeid Alikhani
Department of Mathematical Sciences Yazd University 89195-741 Yazd Iran
19 shared publications - Michael A. Henning
Department of Mathematics and Applied Mathematics University of Johannesburg Auckland Park South Africa
3 shared publications - Ali Sadeghieh
Islamic Azad University
2 shared publications - Mohammad Ali Dehghanizadeh
Department of Mathematics Technical and Vocational University Tehran Iran
2 shared publications - Tuomo Lehtilä
University of Turku
2 shared publications - Abdul Jalil M. Khalaf
Department of Mathematics, Faculty of Computer Science & Mathematics, University of Kufa, Najaf, Iraq
1 shared publication
Latest Publications
- 10 October 2025
- Published by World Scientific Pub Co Pte Ltd in Discrete Mathematics, Algorithms and Applications
- Vol. 18 (09)
Secure domination number of k-subdivision of graphs
Let [ ] be a simple graph. A dominating set of [ ] is a subset [ ] such that every vertex not in [ ] is adjacent to at least one vertex in [ ]. The cardinality of a smallest dominating set of [ ], denoted by [ ], is the domination number of [ ]. A dominating set [ ] is called a secure dominating set of [ ], if for every [ ], there exists a vertex [ ] such that [ ] and [ ] is a dominating set of [ ]. The cardinality of a smallest secure dominating set of [ ], denoted by [ ], is the secure domination number of [ ]. For any [ ], the [ ]-subdivision of [ ] is a simple graph [ ] which is constructed by replacing each edge of [ ] with a path of length [ ]. In this paper, we study the secure domination number of [ ]-subdivision of [ ].
- 10 October 2025
- Published by World Scientific Pub Co Pte Ltd in Discrete Mathematics, Algorithms and Applications
- Vol. 18 (09)
Secure domination number of k-subdivision of graphs
Let [ ] be a simple graph. A dominating set of [ ] is a subset [ ] such that every vertex not in [ ] is adjacent to at least one vertex in [ ]. The cardinality of a smallest dominating set of [ ], denoted by [ ], is the domination number of [ ]. A dominating set [ ] is called a secure dominating set of [ ], if for every [ ], there exists a vertex [ ] such that [ ] and [ ] is a dominating set of [ ]. The cardinality of a smallest secure dominating set of [ ], denoted by [ ], is the secure domination number of [ ]. For any [ ], the [ ]-subdivision of [ ] is a simple graph [ ] which is constructed by replacing each edge of [ ] with a path of length [ ]. In this paper, we study the secure domination number of [ ]-subdivision of [ ].
- 1 January 2025
- Published by University of Zielona Góra, Poland in Discussiones Mathematicae Graph Theory
- Vol. 45 (1) , 21
End super dominating sets in graphs
- 1 January 2025
- Published by University of Zielona Góra, Poland in Discussiones Mathematicae Graph Theory
- Vol. 45 (1) , 21
End super dominating sets in graphs
- 23 December 2024
- Published by World Scientific Pub Co Pte Ltd in Discrete Mathematics, Algorithms and Applications
- Vol. 17 (08)
Strong domatic number of a graph
A set [ ] of vertices of a simple graph [ ] is a strong dominating set, if for every vertex [ ] there is a vertex [ ] with [ ] and [ ]. The strong domination number [ ] is defined as the minimum cardinality of a strong dominating set. The strong domatic number [ ] is the maximum number of strong dominating sets into which the vertex set of [ ] can be partitioned. We initiate the study of the strong domatic number, and we present different sharp bounds on [ ]. In addition, we determine this parameter for some classes of graphs such as cubic graphs of order at most [ ].
- 23 December 2024
- Published by World Scientific Pub Co Pte Ltd in Discrete Mathematics, Algorithms and Applications
- Vol. 17 (08)
Strong domatic number of a graph
A set [ ] of vertices of a simple graph [ ] is a strong dominating set, if for every vertex [ ] there is a vertex [ ] with [ ] and [ ]. The strong domination number [ ] is defined as the minimum cardinality of a strong dominating set. The strong domatic number [ ] is the maximum number of strong dominating sets into which the vertex set of [ ] can be partitioned. We initiate the study of the strong domatic number, and we present different sharp bounds on [ ]. In addition, we determine this parameter for some classes of graphs such as cubic graphs of order at most [ ].
- 11 December 2024
- Published by World Scientific Pub Co Pte Ltd in Discrete Mathematics, Algorithms and Applications
- Vol. 17 (07)
Some results on the super domination number of a graph II
Let [ ] be a simple graph. A dominating set of [ ] is a subset [ ] such that every vertex not in [ ] is adjacent to at least one vertex in [ ]. The cardinality of a smallest dominating set of [ ], denoted by [ ], is the domination number of [ ]. A dominating set [ ] is called a super dominating set of [ ], if for every vertex [ ], there exists [ ] such that [ ]. The cardinality of a smallest super dominating set of [ ], denoted by [ ], is the super domination number of [ ]. In this paper, we obtain more results on the super domination number of graphs which is modified by an operation on vertices. Also, we present some sharp bounds for super domination number of chain and bouquet of pairwise disjoint connected graphs.
- 11 December 2024
- Published by World Scientific Pub Co Pte Ltd in Discrete Mathematics, Algorithms and Applications
- Vol. 17 (07)
Some results on the super domination number of a graph II
Let [ ] be a simple graph. A dominating set of [ ] is a subset [ ] such that every vertex not in [ ] is adjacent to at least one vertex in [ ]. The cardinality of a smallest dominating set of [ ], denoted by [ ], is the domination number of [ ]. A dominating set [ ] is called a super dominating set of [ ], if for every vertex [ ], there exists [ ] such that [ ]. The cardinality of a smallest super dominating set of [ ], denoted by [ ], is the super domination number of [ ]. In this paper, we obtain more results on the super domination number of graphs which is modified by an operation on vertices. Also, we present some sharp bounds for super domination number of chain and bouquet of pairwise disjoint connected graphs.
- Open Access
- 7 August 2024
- Published by University of Nis in Facta Universitatis, Series: Mathematics and Informatics
- Vol. 39 (3) , 469-479
STRONG DOMINATION NUMBER OF HAJÓS SUM AND VERTEX-SUM OF TWO GRAPHS
Let $G=(V,E)$ be a simple graph. A set $D\subseteq V$ is a strong dominating set of $G$, if for every vertex $x\in V\setminus D$ there is a vertex $y\in D$ with $xy\in E(G)$ and $\deg(x)\leq \deg(y)$. The strong domination number $\gst(G)$ is defined as the minimum cardinality of a strong dominating set. In this paper, we study the strong domination number of Haj\'{o}s sum and vertex-sum of two graphs.- 7 August 2024
- Published by University of Nis in Facta Universitatis, Series: Mathematics and Informatics
- Vol. 39 (3) , 469-479
Open AccessSTRONG DOMINATION NUMBER OF HAJÓS SUM AND VERTEX-SUM OF TWO GRAPHS
Let $G=(V,E)$ be a simple graph. A set $D\subseteq V$ is a strong dominating set of $G$, if for every vertex $x\in V\setminus D$ there is a vertex $y\in D$ with $xy\in E(G)$ and $\deg(x)\leq \deg(y)$. The strong domination number $\gst(G)$ is defined as the minimum cardinality of a strong dominating set. In this paper, we study the strong domination number of Haj\'{o}s sum and vertex-sum of two graphs. - Open Access
Elliptic Sombor energy of a graph
Let $G$ be a simple graph with vertex set $V(G) = \{v_1, v_2,\ldots, v_n\}$. The elliptic Sombor matrix of $G$, denoted by $A_{ESO}(G)$, is defined as the $n\times n$ matrix whose $(i,j)$-entry is $(d_i+d_j)\sqrt{d_i^2+d_j^2}$ if $v_i$ and $v_j$ are adjacent and $0$ for another cases. Let the eigenvalues of the elliptic Sombor matrix $A_{ESO}(G)$ be $ρ_1\geq ρ_2\geq \ldots\geq ρ_n$ which are the roots of the elliptic Sombor characteristic polynomial $\prod_{i=1}^n (ρ-ρ_i)$. The elliptic Sombor energy ${E_{ESO}}$ of $G$ is the sum of absolute values of the eigenvalues of $A_{ESO}(G)$. In this paper, we compute the elliptic Sombor characteristic polynomial and the elliptic Sombor energy for some graph classes. We compute the elliptic Sombor energy of cubic graphs of order $10$ and as a consequence, we see that two $k$-regular graphs of the same order may have different elliptic Sombor energy.Open AccessElliptic Sombor energy of a graph
Let $G$ be a simple graph with vertex set $V(G) = \{v_1, v_2,\ldots, v_n\}$. The elliptic Sombor matrix of $G$, denoted by $A_{ESO}(G)$, is defined as the $n\times n$ matrix whose $(i,j)$-entry is $(d_i+d_j)\sqrt{d_i^2+d_j^2}$ if $v_i$ and $v_j$ are adjacent and $0$ for another cases. Let the eigenvalues of the elliptic Sombor matrix $A_{ESO}(G)$ be $ρ_1\geq ρ_2\geq \ldots\geq ρ_n$ which are the roots of the elliptic Sombor characteristic polynomial $\prod_{i=1}^n (ρ-ρ_i)$. The elliptic Sombor energy ${E_{ESO}}$ of $G$ is the sum of absolute values of the eigenvalues of $A_{ESO}(G)$. In this paper, we compute the elliptic Sombor characteristic polynomial and the elliptic Sombor energy for some graph classes. We compute the elliptic Sombor energy of cubic graphs of order $10$ and as a consequence, we see that two $k$-regular graphs of the same order may have different elliptic Sombor energy. - Open Access
- 14 February 2024
- Published by Elsevier in Discrete Applied Mathematics
- Vol. 349, 8-24
Super domination: Graph classes, products and enumeration
- 14 February 2024
- Published by Elsevier in Discrete Applied Mathematics
- Vol. 349, 8-24
Open AccessSuper domination: Graph classes, products and enumeration
- Open Access
Co-even Domination Number of a Modified Graph by Operations on a Vertex or an Edge
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 a smallest dominating set of $G$, denoted by $\gamma(G)$, is the domination number of $G$. A dominating set $D$ is called co-even dominating set if the degree of vertex $v$ is even number for all $v\in V-D$. The cardinality of a smallest co-even dominating set of $G$, denoted by $\gamma _{coe}(G)$, is the co-even domination number of $G$. In this paper we study co-even domination number of graphs which constructed by some operations on a vertex or an edge of a graph.Open AccessCo-even Domination Number of a Modified Graph by Operations on a Vertex or an Edge
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 a smallest dominating set of $G$, denoted by $\gamma(G)$, is the domination number of $G$. A dominating set $D$ is called co-even dominating set if the degree of vertex $v$ is even number for all $v\in V-D$. The cardinality of a smallest co-even dominating set of $G$, denoted by $\gamma _{coe}(G)$, is the co-even domination number of $G$. In this paper we study co-even domination number of graphs which constructed by some operations on a vertex or an edge of a graph. - 1 January 2024
- Published by Taru Publications in Journal of Discrete Mathematical Sciences and Cryptography
- Vol. 27 (3) , 983-998
Sombor polynomial (function) of a graph
- 1 January 2024
- Published by Taru Publications in Journal of Discrete Mathematical Sciences and Cryptography
- Vol. 27 (3) , 983-998
Sombor polynomial (function) of a graph
- Open Access
Strong domination number of graphs from primary subgraphs
A set $D$ of vertices is a strong dominating set in a graph $G$, if for every vertex $x\in V(G) \setminus D$ there is a vertex $y\in D$ with $xy\in E(G)$ and $deg(x) \leq deg(y)$. The strong domination number $γ_{st}(G)$ of $G$ is the minimum cardinality of a strong dominating set in $G$. Let $G$ be a connected graph constructed from pairwise disjoint connected graphs $G_1,\ldots ,G_k$ by selecting a vertex of $G_1$, a vertex of $G_2$, and identifying these two vertices, and thereafter continuing in this manner inductively. The graphs $G_1,\ldots ,G_k$ are the primary subgraphs of $G$. In this paper, we study the strong domination number of $K_r$-gluing of two graphs and investigate the strong domination number for some particular cases of graphs from their primary subgraphs.Open AccessStrong domination number of graphs from primary subgraphs
A set $D$ of vertices is a strong dominating set in a graph $G$, if for every vertex $x\in V(G) \setminus D$ there is a vertex $y\in D$ with $xy\in E(G)$ and $deg(x) \leq deg(y)$. The strong domination number $γ_{st}(G)$ of $G$ is the minimum cardinality of a strong dominating set in $G$. Let $G$ be a connected graph constructed from pairwise disjoint connected graphs $G_1,\ldots ,G_k$ by selecting a vertex of $G_1$, a vertex of $G_2$, and identifying these two vertices, and thereafter continuing in this manner inductively. The graphs $G_1,\ldots ,G_k$ are the primary subgraphs of $G$. In this paper, we study the strong domination number of $K_r$-gluing of two graphs and investigate the strong domination number for some particular cases of graphs from their primary subgraphs.