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Mohsen Ghasemi

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Papers by Mohsen Ghasemi

A note on codegrees and Taketa's inequality

Let G be a finite group and cd(G) will be the set of the degrees of the complex irreducible chara... more Let G be a finite group and cd(G) will be the set of the degrees of the complex irreducible characters of G. Also let cod(G) be the set of codegrees of the irreducible characters of G. The Taketa problem conjectures if G is solvable, then dl(G) ≤ |cd(G)|, where dl(G) is the derived length of G. In this note, we show that dl(G) ≤ |cod(G)| in some cases and we conjecture that this inequality holds if G is a finite solvable group.

Tetravalent s-transitive graphs of order $6p^2$

arXiv (Cornell University), Oct 1, 2022

Let s be a positive integer. A graph is s-transitive if its automorphism group is transitive on s... more

A family of tetravalent one-regular graphs

arXiv (Cornell University), Aug 9, 2021

A graph is one-regular if its automorphism group acts regularly on the set of its arcs. In this p... more

Groups which do not have four irreducible characters of degrees divisible by a prime p

Journal of Pure and Applied Algebra, 2019

Please cite this article in press as: F. Alizadeh et al., Groups which do not have four irreducib... more

Finite groups whose codegrees are almost prime

Communications in Algebra, 2020

For a character v of a finite group G, the number codðvÞ ¼ jG : kerðvÞj=vð1Þ is called the codegr... more For a character v of a finite group G, the number codðvÞ ¼ jG : kerðvÞj=vð1Þ is called the codegree of v. In this paper we show that if G is nonsolvable, then the codegree graph CðGÞ has a triangle. Also by using this result we show that if G has one composite codegree, then G is solvable and jcodðGÞj 5: ARTICLE HISTORY

On the super connectivity of direct product of graphs

RAIRO - Operations Research

A vertex-cut S is called a super vertex-cut if G − S is disconnected and it contains no isolated ... more A vertex-cut S is called a super vertex-cut if G − S is disconnected and it contains no isolated vertices. The super-connectivity, κ′, is the minimum cardinality over all super vertex-cuts. This article provides bounds for the super connectivity of the direct product of an arbitrary graph and the complete graph Kn. Among other results, we show that if G is a non-complete graph with girth(G) = 3 and κ′(G) = ∞, then κ′(G × Kn) ≤ min{mn − 6, m(n − 1) + 5, 5n + m − 8}, where |V(G)| = m.

Some Tetravalent One-Regular Graphs of Special Order

Mathematical Researches

CUBIC SYMMETRIC GRAPHS OF ORDER 10p

An automorphism group of a graph is said to be s-regular if it acts regularly on the set of s-arc... more

On the Normality of Some Cayley Digraphs with Valency 2

Journal of the Indonesian Mathematical Society, 2011

We call a Cayley digraph 􀀀=Cay(G; S) normal for G if R(G), the rightregular representation of G, ... more We call a Cayley digraph 􀀀=Cay(G; S) normal for G if R(G), the rightregular representation of G, is a normal subgroup of the full automorphism groupAut(􀀀) of 􀀀. In this paper we determine the normality of Cayley digraphs of valency2 on the groups of order pq and also on non-abelian nite groups G such that everyproper subgroup of G is abelian.DOI : http://dx.doi.org/10.22342/jims.17.2.3.67-72

The normality of cubic Cayley graphs for dihedral groups

A Cayley graph Γ = Cay(G, S) is called normal for G, if GR, the right regular representation of G... more

Nonnormal Edge-Transitive Cubic Cayley Graphs of Dihedral Groups

ISRN Algebra, 2011

A Cayley graph of a finite group is called normal edge transitive if its automorphism group has a... more A Cayley graph of a finite group is called normal edge transitive if its automorphism group has a subgroup which both normalizes and acts transitively on edges. In this paper we determine all cubic, connected, and undirected edge-transitive Cayley graphs of dihedral groups, which are not normal edge transitive. This is a partial answer to the question of Praeger (1999).

Tetravalent vertex-transitive graphs of order $6p$

A graph is vertex-transitive if its automorphism group acts transitively on vertices of the graph... more A graph is vertex-transitive if its automorphism group acts transitively on vertices of the graph. A vertex-transitive graph is a Cayley graph if its automorphism group contains a subgroup acting regularly on its vertices. In this paper, the tetravalent vertex-transitive non-Cayley graphs of order 6p are classified for each prime p. 1. Introduction In this paper we consider undirected finite connected graphs without loops or multiple edges. For a graph X we use V (X), E(X), A(X) and Aut(X) to denote its vertex set, edge set, arc set and its full automorphism group, respectively. For u, v ∈ V (X), u ∼ v represents that u is adjacent to v, and is denoted by {u, v} the edge incident to u and v in X, and N X (u) is the neighborhood of u in X, that is, the set of vertices adjacent to u in X. A graph X is said to be G-vertex-transitive, G-edge-transitive and G-arctransitive (or G-symmetric) if G ≤ Aut(X) acts transitively on V (X), E(X) and A(X), respectively. In the special case, if G = Aut(X) then X is said to be vertex-transitive, edge-transitive and arc-transitive (or symmetric). An s-arc in a graph X is an ordered (s + 1)-tuple (v 0 , v 1 , • • • , v s) of vertices of X such that v i−1 is adjacent to v i for 1 ≤ i ≤ s, and v i−1 = v i+1 for 1 ≤ i ≤ s; in other words, a directed walk of length s which never includes a backtracking. A graph X is said to be s-arc-transitive if Aut(X) is transitive on the set of s-arcs in X. A subgroup of the automorphism group of a graph X is said to be s-regular if it acts regularly on the set of s-arcs of X. Recall that a permutation group G acting on a set Ω is called semiregular if the stabilizer of α ∈ G, G α = 1 for all α ∈ G and is called regular if it is semiregular and transitive.

Normality of one-matching semi-Cayley graphs over finite abelian groups with maximum degree 3

Contributions Discret. Math., 2020

A graph $\Gamma$ is said to be a semi-Cayley graph over a group $G$ if it admits $G$ as a semireg... more A graph $\Gamma$ is said to be a semi-Cayley graph over a group $G$ if it admits $G$ as a semiregular automorphism group with two orbits of equal size. We say that $\Gamma$ is normal if $G$ is a normal subgroup of ${\rm Aut}(\Gamma)$. We prove that every connected intransitive one-matching semi-Cayley graph, with maximum degree three, over a finite abelian group is normal and characterize all such non-normal graphs.

Super connectivity of lexicographic product graphs

arXiv: Combinatorics, 2020

For a graph $G$, $k(G)$ denotes its connectivity. A graph is super connected if every minimum ver... more For a graph $G$, $k(G)$ denotes its connectivity. A graph is super connected if every minimum vertex-cut isolates a vertex. Also $k_{1}$-connectivity of a connected graph is the minimum number of vertices whose deletion gives a disconnected graph without isolated vertices. This paper provides bounds for the super connectivity and $k_{1}$-connectivity of the lexicographic product of two graphs.

Equivalent version of Huppert's conjecture for $K_3$-groups

For a character χ of a finite groupG the number cod(χ) = |G : Ker(χ)|/χ(1) is called the codegree... more

Recognition of Janko groups and some simple $K_4$-groups by the order and one irreducible character degree or character degree graph

International Journal of Group Theory, 2019

In this paper we prove that some Janko groups are uniquely determined by their orders and one irr... more

Isomorphisms of bi-Cayley graphs on Dihedral groups

Discrete Mathematics, Algorithms and Applications, 2020

For a group [Formula: see text] and a subset [Formula: see text] of [Formula: see text] the bi-Ca... more For a group [Formula: see text] and a subset [Formula: see text] of [Formula: see text] the bi-Cayley graph BCay[Formula: see text] of [Formula: see text] with respect to [Formula: see text] is the bipartite graph with vertex set [Formula: see text] and edge set [Formula: see text]. A bi-Cayley graph BCay[Formula: see text] is called a BCI-graph if for any bi-Cayley graph BCay[Formula: see text], [Formula: see text] implies that [Formula: see text] for some [Formula: see text] and [Formula: see text]. A group [Formula: see text] is called a [Formula: see text]-BCI-group if all bi-Cayley graphs of [Formula: see text] with valency at most [Formula: see text] are BCI-graphs. In this paper, we characterize the [Formula: see text]-BCI dihedral groups for [Formula: see text]. Also, we show that the dihedral group [Formula: see text] ([Formula: see text] is prime) is a [Formula: see text]-BCI-group.

A classification of tetravalent arc-transitive graphs of order 5p2

Indian Journal of Pure and Applied Mathematics, 2020

Let s be a positive integer. A graph is s-transitive if its automorphism group is transitive on s... more

An Algorithmic-type Classification of Tetravalent One-regular Graphs Using Computer Algebra Tools

Fundamenta Informaticae, 2014

Resumen En este trabajo presentamos el procedimiento de construcción de un cuestionario de dilema... more Resumen En este trabajo presentamos el procedimiento de construcción de un cuestionario de dilemas que indaga las teorías implícitas de aprendizaje a partir de la lectura en estudiantes universitarios. Para su elaboración se consideraron dimensiones y categorías definidas desde desarrollos teóricos sobre teorías implícitas de aprendizaje y teorías científicas sobre la lectura. En tanto que desde la perspectiva empírica se atendió a las voces de los estudiantes; esto contribuyó a una formulación más ajustada tanto de los dilemas como de las diferentes opciones de resolución de los mismos, y orientó la selección de los escenarios educativos en los que éstos se enmarcan. La validez del instrumento se determinó mediante el proceso de control de expertos. Para establecer la confiabilidad se aplicó el coeficiente de Cronbach. Los índices de validez y confiabilidad obtenidos demuestran que el cuestionario está dentro de los valores requeridos, para ser administrado a los estudiantes. Palabras clave: cuestionario de dilemas, concepciones de aprendizaje, lectura, ingresantes universitarios.

Tetravalent Vertex-Transitive Graphs of Order Twice A Prime Square

Graphs and Combinatorics, 2016

A graph is vertex-transitive if its automorphism group acts transitively on vertices of the graph... more A graph is vertex-transitive if its automorphism group acts transitively on vertices of the graph. A vertex-transitive graph is a Cayley graph if its automorphism group contains a subgroup acting regularly on its vertices. In this paper, a complete classification is given of tetravalent vertex-transitive non-Cayley graphs of order $$2p^2$$2p2 for any prime p.