3 citations · 3 across the 2 of their papers we have counts for
6 papers
On the structure of the power graph and the enhanced power graph of a group
Ghodratollah Aalipour, Saieed Akbari, Peter J. Cameron +2
Let be a group. The \emph{power graph} of is a graph with the vertex set , having an edge between two elements whenever one is a power of the other. We characterize nilp…
A weighted cellular matrix-tree theorem, with applications to complete colorful and cubical complexes
Ghodratollah Aalipour, Art M. Duval, Woong Kook +2
We present a version of the weighted cellular matrix-tree theorem that is suitable for calculating explicit generating functions for spanning trees of highly structured families of…
On the distance spectra of graphs
Ghodratollah Aalipour, Aida Abiad, Zhanar Berikkyzy +8
The distance matrix of a graph is the matrix containing the pairwise distances between vertices. The distance eigenvalues of are the eigenvalues of its distance matrix and…
Proof of a conjecture of Graham and Lovász concerning unimodality of coefficients of the distance characteristic polynomial of a tree
Ghodratollah Aalipour, Aida Abiad, Zhanar Berikkyzy +4
We establish a conjecture of Graham and Lovász that the (normalized) coefficients of the distance characteristic polynomial of a tree are unimodal; we also prove they are log-conca…
Application of some combinatorial arrays in coloring of total graph of a commutative ring
Ghodratollah Aalipour, Saieed Akbari
Let be a commutative ring with unity and and be the set of zero-divisors and non-zero zero-divisors of , respectively. We denote by , the tota…
On the Cayley graph of a commutative ring with respect to its zero-divisors
Ghodratollah Aalipour, Saieed Akbari
Let be a commutative ring with unity and be be the additive group and the set of all non-zero zero-divisors of , respectively. We denote by $\mathbb{CAY}(R)…