42 citations · 121 across the 18 of their papers we have counts for
24 papers
On the In-Out-Proper Orientations of Graphs
Ali Dehghan
An orientation of a graph is {\it in-out-proper} if any two adjacent vertices have different in-out-degrees, where the in-out-degree of each vertex is equal to the in-degree mi…
On the maximum number of non attacking rooks on a high-dimensional simplicial chessboard
Arash Ahadi, Mohsen Mollahajiaghaei, Ali Dehghan
The simplicial rook graph is the graph whose vertices are vectors in such that for each vector the summation of its coordinates is and…
Cospectral Bipartite Graphs with the Same Degree Sequences but with Different Number of Large Cycles
Ali Dehghan, Amir H. Banihashemi
Finding the multiplicity of cycles in bipartite graphs is a fundamental problem of interest in many fields including the analysis and design of low-density parity-check (LDPC) code…
On the semi-proper orientations of graphs
Ali Dehghan
A {\it semi-proper orientation} of a given graph is a function that assigns an orientation and a positive integer weight to each edge such that for e…
On Computing the Number of Short Cycles in Bipartite Graphs Using the Spectrum of the Directed Edge Matrix
Ali Dehghan, Amir H. Banihashemi
Counting short cycles in bipartite graphs is a fundamental problem of interest in many fields including the analysis and design of low-density parity-check (LDPC) codes. There are…
On Computing the Multiplicity of Cycles in Bipartite Graphs Using the Degree Distribution and the Spectrum of the Graph
Ali Dehghan, Amir H. Banihashemi
Counting short cycles in bipartite graphs is a fundamental problem of interest in the analysis and design of low-density parity-check (LDPC) codes. The vast majority of research in…
On the algorithmic complexity of decomposing graphs into regular/irregular structures
Arash Ahadi, Ali Dehghan, Mohammad-Reza Sadeghi +1
A locally irregular graph is a graph whose adjacent vertices have distinct degrees, a regular graph is a graph where each vertex has the same degree and a locally regular graph is…
Not-All-Equal and 1-in-Degree Decompositions: Algorithmic Complexity and Applications
Ali Dehghan, Mohammad-Reza Sadeghi, Arash Ahadi
A Not-All-Equal (NAE) decomposition of a graph is a decomposition of the vertices of into two parts such that each vertex in has at least one neighbor in each part. Als…
Hardness Results on Finding Leafless Elementary Trapping Sets and Elementary Absorbing Sets of LDPC Codes
Ali Dehghan, Amir H. Banihashemi
Leafless elementary trapping sets (LETSs) are known to be the problematic structures in the error floor region of low-density parity-check (LDPC) codes over the additive white Gaus…
From Cages to Trapping Sets and Codewords: A Technique to Derive Tight Upper Bounds on the Minimum Size of Trapping Sets and Minimum Distance of LDPC Codes
Ali Dehghan, Amir H. Banihashemi
Cages, defined as regular graphs with minimum number of nodes for a given girth, are well-studied in graph theory. Trapping sets are graphical structures responsible for error floo…
Asymptotic Average Multiplicity of Structures within Different Categories of Trapping Sets, Absorbing Sets and Stopping Sets in Random Regular and Irregular LDPC Code Ensembles
Ali Dehghan, Amir H. Banihashemi
The performance of low-density parity-check (LDPC) codes in the error floor region is closely related to some combinatorial structures of the code's Tanner graph, collectively refe…
Is there any polynomial upper bound for the universal labeling of graphs?
Arash Ahadi, Ali Dehghan, Morteza Saghafian
A {\it universal labeling} of a graph is a labeling of the edge set in such that in every orientation of for every two adjacent vertices and , the sum of…
Algorithmic complexity of proper labeling problems
Ali Dehghan, Mohammad-Reza Sadeghi, Arash Ahadi
A proper labeling of a graph is an assignment of integers to some elements of a graph, which may be the vertices, the edges, or both of them, such that we obtain a proper vertex co…
Algorithmic Complexity of Weakly Semiregular Partitioning and the Representation Number
Arash Ahadi, Ali Dehghan, Mohsen Mollahajiaghaei
A graph is {\it weakly semiregular} if there are two numbers , such that the degree of every vertex is or . The {\it weakly semiregular number} of a graph , deno…
On the Tanner Graph Cycle Distribution of Random LDPC, Random Protograph-Based LDPC, and Random Quasi-Cyclic LDPC Code Ensembles
Ali Dehghan, Amir H. Banihashemi
In this paper, we study the cycle distribution of random low-density parity-check (LDPC) codes, randomly constructed protograph-based LDPC codes, and random quasi-cyclic (QC) LDPC…
On the algorithmic complexity of adjacent vertex closed distinguishing colorings number of graphs
Ali Dehghan, Mohsen Mollahajiaghaei
An assignment of numbers to the vertices of graph G is closed distinguishing if for any two adjacent vertices v and u the sum of labels of the vertices in the closed neighborhood o…
Examples of interacting particle systems on as Pfaffian point processes: coalescing branching random walks and annihilating random walks with immigration
Barnaby Garrod, Roger Tribe, Oleg Zaboronski
Two classes of interacting particle systems on are shown to be Pfaffian point processes at fixed times, and for all deterministic initial conditions. The first compris…
On the complexity of deciding whether the regular number is at most two
Ali Dehghan, Mohammad-Reza Sadeghi, Arash Ahadi
The regular number of a graph G denoted by reg(G) is the minimum number of subsets into which the edge set of G can be partitioned so that the subgraph induced by each subset is re…
Sigma Partitioning: Complexity and Random Graphs
Ali Dehghan, Mohammad-Reza Sadeghi, Arash Ahadi
A of a graph is a partition of the vertices into sets such that for every two adjacent vertices and there is an index $…
The inapproximability for the (0,1)-additive number
Arash Ahadi, Ali Dehghan
An {\it additive labeling} of a graph is a function , such that for every two adjacent vertices and of , $ \sum_{w \sim v}\el…
The Complexity of the Proper Orientation Number
Arash Ahadi, Ali Dehghan
Graph orientation is a well-studied area of graph theory. A proper orientation of a graph is an orientation of such that for every two adjacent vertices $ v…
On the Lucky labeling of Graphs
Arash Ahadi, Ali Dehghan, Esmael Mollaahmadi
Suppose the vertices of a graph were labeled arbitrarily by positive integers, and let denote the sum of labels over all neighbors of vertex . A labeling is lucky i…
On Rainbow Connection of Strongly Regular Graphs
Arash Ahadi, Ali Dehghan
An edge-colored graph is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph ,…
Upper bounds for the 2-hued chromatic number of graphs in terms of the independence number
Arash Ahadi, Ali Dehghan
A 2-hued coloring of a graph (also known as conditional -coloring and dynamic coloring) is a coloring such that for every vertex of degree at least , the…