4 citations · 10 across the 12 of their papers we have counts for
13 papers
Finite groups with quadratic splitting fields for all Cayley graphs
Majid Arezoomand, Alireza Abdollahi, Tao Feng +1
For a graph , the splitting field of is defined as the splitting field of the characteristic polynomial of over rationals. The algebraic degree of is defined by the…
Perfect codes and regular sets in vertex-transitive graphs
Alireza Abdollahi, Zeinab Akhlaghi, Majid Arezoomand
A subset \( C \) of the vertex set \( V \) of a graph \( Γ= (V,E) \) is termed an -regular set if each vertex in \( C \) is adjacent to exactly \( r \) other vertices in \(…
On -integral Cayley graphs
Alireza Abdollahi, Majid Arezoomand, Tao Feng +1
In this paper, we introduce the concept of -integral graphs. A graph is called -integral if the extension degree of the splitting field of the characteristic polynomial o…
Algebraic degrees of quasi-abelian semi-Cayley digraphs
Shixin Wang, Majid Arezoomand, Tao Feng
For a digraph , if is the smallest field that contains all roots of the characteristic polynomial of the adjacency matrix of , then is called the splitting field of $…
Integral Cayley graphs of symmetric groups on transpositions
Alireza Abdollahi, Majid Arezoomand, Mahdi Ebrahimi
We study subsets consisting of some transpositions of the symmetric group on such that the Cayley graph is an integral graph, i.…
Tetravalent vertex-transitive graphs of order
Majid Arezoomand, Mohsen Ghasemi, Mohammad A. Iranmanesh
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…
Perfect state transfer on semi-Cayley graphs over abelian groups
Majid Arezoomand
In this paper, we consider the problem on the existence of perfect state transfer(PST for short) on semi-Cayley graphs over abelian groups (which are not necessarily regular), i.e…
Totally -closed finite groups with trivial Fitting subgroup
Majid Arezoomand, Mohammad A. Iranmanesh, Cheryl E. Praeger +1
A group is said to be totally -closed if in each of its faithful permutation representations, say on a set , is the largest subgroup of which leaves…
Fixity of elusive groups and the polycirculant conjecture
Majid Arezoomand
Let be transitive. Then is called \textit{elusive} on if it has no fixed point free element of prime order. The \textit{-closure} of , denoted by…
Normality of one-matching semi-Cayley graphs over finite abelian groups with maximum degree three
Majid Arezoomand, Mohsen Ghasemi
A graph is said to be a semi-Cayley graph over a group if it admits as a semiregular automorphism group with two orbits of equal size. We say that is normal if …
On $\BCI$-groups and $\CI$-groups
Asieh Sattari, Majid Arezoomand, Mohammad A. Iranmanesh
Let be a finite group and be a subset of A bi-Cayley graph $\BCay(G,S)$ is a simple and an undirected graph with vertex-set and edge-set $\{\{(g,1),(s…
On finite totally 2-closed groups
Alireza Abdollahi, Majid Arezoomand, Gareth Tracey
An abstract group is called totally -closed if for any set with , where is the largest subgroup of who…
Finite nilpotent groups coincide with their -closures in all of their faithful permutation representations
Alireza Abdollahi, Majid Arezoomand
Here we show that a finite nilpotent group is 2-closed if and only if it is either cyclic or a direct product of a generalized quaternion group with a cyclic group of odd order.