M. F. D. Ghouchan

activity

20142025

most citedToroidal and projective commuting and non-commuting graphs

10 citations · 19 across the 18 of their papers we have counts for

collaborators

20 papers

math.CO2025

Positive matching decompositions of the cartesian product of graphs

Mohammad Farrokhi Derakhshandeh Ghouchan, Ali Akbar Yazdan Pour

Let $Γ = (V, E)$ be a finite simple graph. A matching $M \subseteq E$ is positive if there exists a weight function on $V$ such that the matching $M$ is characterized by those edges w…

math.CO2023

Explicit formulas for matrices associated to ladder, circular ladder, and Mobius ladder graphs

Ali Azimi, Mohammad Farrokhi Derakhshandeh Ghouchan

We give explicit formulas for resistance distance matrices and Moore-Penrose inverses of incidence and Laplacian matrices of ladder, circular ladder, and Möbius ladder graphs. As a…

math.AC2023

Gröbner basis and Krull dimension of Lovász-Saks-Sherijver ideal associated to a tree

Mohammad Farrokhi Derakhshandeh Ghouchan, Ali Akbar Yazdan Pour

Let $K$ be a field and $n$ be a positive integer. Let $Γ = ([n], E)$ be a simple graph, where $[n] = {1, \dots, n}$ . If $S = K [x_{1}, \dots, x_{n}, y_{1}, \dots, y_{n}]$ is…

math.CO2023

Moore-Penrose inverse of incidence matrices

Ali Azimi, R. B. Bapat, Mohammad Farrokhi Derakhshandeh Ghouchan

We present explicit formulas for Moore-Penrose inverses of some families of set inclusion matrices arising from sets, vector spaces, and designs.

math.AC2022

Cellular resolutions of monomial ideals and their Artinian reductions

Sara Faridi, Mohammad Farrokhi Derakhshandeh Ghouchan, Roghayyeh Ghorbani +1

The question we address in this paper is: which monomial ideals have minimal cellular resolutions, that is, minimal resolutions obtained from homogenizing the chain maps of CW-comp…

math.CO2022

Fully reducible simple Venn diagrams

Mohammad Farrokhi Derakhshandeh Ghouchan

We generalize Venn diagrams in spaces of arbitrary dimension $\geq 2$ and study simple Venn diagrams with the reducing property. Three equivalent conditions for a simple Venn diagr…

math.AC2021

Extending simplicial complexes: Topological and combinatorial properties

Mohammad Farrokhi Derakhshandeh Ghouchan, Alireza Shamsian, Ali Akbar Yazdan Pour

Given an arbitrary hypergraph $H$ , we may glue to $H$ a family of hypergraphs to get a new hypergraph $H^{'}$ having $H$ as an induced subhyper…

math.CO2021

Positive matching decompositions of graphs

Mohammad Farrokhi Derakhshandeh Ghouchan, Shekoofeh Gharakhloo, Ali Akbar Yazdan Pour

A matching $M$ in a graph $Γ$ is positive if $Γ$ has a vertex-labeling such that $M$ coincides with the set of edges with positive weights. A positive matching decomposition (pmd)…

math.GR2019

Finite groups with five relative commutativity degrees

Mohammad Farrokhi Derakhshandeh Ghouchan

We classify all finite groups with five relative commutativity degrees. Also, we give a partial answer to our previous conjecture on a lower bound of the number of relative commuta…

math.GR2019

Factorization graphs of finite groups

Mohammad Farrokhi Derakhshandeh Ghouchan, Ali Azimi

We introduce the factorization graph of a finite group and study its connectedness and forbidden structures. We characterize all finite groups with connected factorization graphs a…

math.CO2019

Lattice paths inside a table: Rows and columns linear combinations

Mohammad Farrokhi Derakhshandeh Ghouchan

A lattice path inside the $m \times n$ table $T$ is a sequence $ν_{1}, \dots, ν_{k}$ of cells such that $ν_{j + 1} - ν_{j} \in {(1, - 1), (1, 0), (1, 1)}$ for all $j = 1, \dots, k - 1$ . The number of lat…

math.CO2019

Some Algebraic Properties of Sierpiński-Type Graphs

Mohammad Farrokhi Derakhshandeh Ghouchan, E. Ghorbani, H. R. Maimani +1

This paper deals with some of the algebraic properties of Sierpiński graphs and a family of regular generalized Sierpiński graphs. For the family of regular generalized Sierpiński…

math.GM2017

Lattice paths inside a table, II

Daniel Yaqubi, Mohammad Farrokhi Derakhshandeh Ghouchan, Mohamad Zamani khademanlu

Consider an $m \times n$ table $T$ and latices paths $ν_{1}, \dots, ν_{k}$ in $T$ such that each step $ν_{i + 1} - ν_{i} = (1, 1)$ , $(1, 0)$ or $(1, - 1)$ . The number of paths from the $(1, i)$ -blank…

math.CO2016

A characterization of Tutte-Coxeter graph

Mohammad Farrokhi Derakhshandeh Ghouchan, Abbas Mohammadian

We give a natural generalization of the Tutte-Coxeter graph in a natural way and prove that the Tutte-Coxeter graph is the only vertex-transitive (edge-transitive) graph among all…

math.GR2014★ 10 cited

Toroidal and projective commuting and non-commuting graphs

Mojgan Afkhami, Mohammad Farrokhi Derakhshandeh Ghouchan, Kazem Khashyarmanesh

In this paper, all finite groups whose commuting (non-commuting) graphs can be embed on the plane, torus or projective plane are classified.

math.GR2014★ 7 cited

Embeddings of (proper) power graphs of finite groups

Alireza Doostabadi, Mohammad Farrokhi Derakhshandeh Ghouchan

The (proper) power graph of a group is a graph whose vertex set is the set of all (nontrivial) elements of the group and two distinct vertices are adjacent if one is a power of the…

math.GR2014

On the connectivity of proper power graphs of finite groups

Alireza Doostabadi, Mohammad Farrokhi Derakhshandeh Ghouchan

We study the connectivity of proper power graphs of some family of finite groups including nilpotent groups, groups with a non-trivial partition, and symmetric and alternating grou…

math.GR2014

On power graphs of finite groups with forbidden induced subgraphs

Alireza Doostabadi, Ahmad Erfanian, Mohammad Farrokhi Derakhshandeh Ghouchan

The power graph $P (G)$ of a finite group $G$ is a graph whose vertex set is the group $G$ and distinct elements $x, y \in G$ are adjacent if one is a power of the other, th…

math.AC2014

On cycles in intersection graph of rings

Ali Azimi, Ahmad Erfanian, Mohammad Farrokhi Derakhshandeh Ghouchan +1

Let $R$ be a commutative ring with non-zero identity. We describe all $C_{3}$ - and $C_{4}$ -free intersection graph of non-trivial ideals of $R$ as well as $C_{n}$ -free intersection graph…

math.AC2014★ 2 cited

Cycles and paths in Jacobson graphs

Ali Azimi, Mohammad Farrokhi Derakhshandeh Ghouchan

All finite Jacobson graphs with a Hamiltonian cycle or path, or Eulerian tour or trail are determined, and it is shown that a finite Jacobson graph is Hamiltonian if and only if it…