1 citations · 2 across the 19 of their papers we have counts for
19 papers
-Neighbor Bootstrap Percolation on Odd Graphs
Ali Mohammadian, Sina Rezaie Zareie, Behruz Tayfeh-Rezaie
The -neighbor bootstrap percolation process on a graph is a vertex-activation process that begins with a set of initially active vertices. In each subsequent round, every in…
A search for Hadamard matrices of Williamson type
Hadi Kharaghani, Ali Mohammadian, Behruz Tayfeh-Rezaie
In this article, we consider a special class of Williamson type matrices which we call them near Williamson matrices. They are in fact four -matrices $A, B, C,…
On saturation numbers of complete multipartite graphs and even cycles
Ali Mohammadian, Milad Poursoltani, Behruz Tayfeh-Rezaie
Given positive integer and graph , the saturation number is the minimum number of edges in an edge-maximal -free graph on vertices. In this paper…
Bootstrap percolation on the Hamming graphs
Meysam Miralaei, Ali Mohammadian, Behruz Tayfeh-Rezaie
The -edge bootstrap percolation on a graph is an activation process of the edges. The process starts with some initially activated edges and then, in each round, any inactive ed…
On the classification of skew Hadamard matrices of order 36 and related structures
Makoto Araya, Masaaki Harada, Hadi Kharaghani +2
Two skew Hadamard matrices are considered {\sf SH}-equivalent if they are similar by a signed permutation matrix. This paper determines the number of {\sf SH}-inequivalent skew Had…
Weak saturation numbers in random graphs
Olga Kalinichenko, Meysam Miralaei, Ali Mohammadian +1
For two given graphs and , a graph is said to be weakly -saturated if is a spanning subgraph of which has no copy of as a subgraph and one can ad…
Saturation numbers of bipartite graphs in random graphs
Meysam Miralaei, Ali Mohammadian, Behruz Tayfeh-Rezaie +1
For a given graph , the -saturation number of a graph , denoted by , is the minimum number of edges in an edge-maximal -free subgraph of . In 2017, Kor…
The weak saturation number of
Meysam Miralaei, Ali Mohammadian, Behruz Tayfeh-Rezaie
For two graphs and , we say that is weakly -saturated if contains no copy of as a subgraph and one could join all the nonadjacent pairs of vertices of in…
On the location of zeros of the Laplacian matching polynomials of graphs
Jiang-Chao Wan, Yi Wang, Ali Mohammadian
The Laplacian matching polynomial of a graph , denoted by , is a new graph polynomial whose all roots are nonnegative real numbers. In this pap…
Threshold for weak saturation stability
M. Bidgoli, A. Mohammadian, B. Tayfeh-Rezaie +1
We study the weak -saturation number of the Erdős--Rényi random graph $\mathbbmsl{G}(n, p)$, denoted by $\mathrm{wsat}(\mathbbmsl{G}(n, p), K_s)$, where is the complete…
Percolating sets in bootstrap percolation on the Hamming graphs
M. R. Bidgoli, A. Mohammadian, B. Tayfeh-Rezaie
For any integer , the -neighbor bootstrap percolation on a graph is an activation process of the vertices. The process starts with some initially activated vertices…
On -bootstrap percolation
M. R. Bidgoli, A. Mohammadian, B. Tayfeh-Rezaie
Given two graphs and , it is said that percolates in -bootstrap process if one could join all the nonadjacent pairs of vertices of in some order such that a new c…
Star Saturation Number of Random Graphs
A. Mohammadian, B. Tayfeh-Rezaie
For a given graph , the -saturation number of a graph is the minimum number of edges in an edge-maximal -free subgraph of . Recently, the -saturation number of t…
Hadamard matrices with few distinct types
A. Mohammadian, B. Tayfeh-Rezaie
The notion of type of quadruples of rows is proven to be useful in the classification of Hadamard matrices. In this paper, we investigate Hadamard matrices with few distinct types.…
Maximum order of triangle-free graphs with a given rank
E. Ghorbani, A. Mohammadian, B. Tayfeh-Rezaie
The rank of a graph is defined to be the rank of its adjacency matrix. A graph is called reduced if it has no isolated vertices and no two vertices with the same set of neighbors.…
On a family of diamond-free strongly regular graphs
A. Mohammadian, B. Tayfeh-Rezaie
The existence of a partial quadrangle is equivalent to the existence of a diamond-free strongly regular graph ${\mathsf{SRG}}(1+s(t+1)+s^2t(t+1)/μ, s(t+1),…
Integral trees with given nullity
E. Ghorbani, A. Mohammadian, B. Tayfeh-Rezaie
A graph is called integral if all eigenvalues of its adjacency matrix consist entirely of integers. We prove that for a given nullity more than 1, there are only finitely many inte…
On Order and Rank of Graphs
E. Ghorbani, A. Mohammadian, B. Tayfeh-Rezaie
The rank of a graph is defined to be the rank of its adjacency matrix. A graph is called reduced if it has no isolated vertices and no two vertices with the same set of neighbors.…
Integral trees of odd diameters
E. Ghorbani, A. Mohammadian, B. Tayfeh-Rezaie
A graph is called integral if all eigenvalues of its adjacency matrix consist entirely of integers. Recently, Csikvari proved the existence of integral trees of any even diameter.…