Teaching Activities

I regularely teach the following courses:
1. Graph Theory, References: "An Introduction to Graph Theory" by D. West and "Graph Theory" by R. Diestel
2. Algorithmic Graph Theory
3. Probabilistic Method in Graph Theory
4. Source Coding and Error Correcting Codes, References: "Elements of Information Theory" By T. Cover, "Information and Coding Theory" by G. A. Jones and J. M. Jones and "Coding theory" by W. J. Korner
5. Cryptography, Reference: "Cryptography: Theory and Practice" by D. Stinson

Research Areas:

Chromatic graph theory, extremal graph theory, algorithms and complexity of graph problems, applications of graph theory in social networks, influence phenomena in social networks, the probabilistic methods in graph theory, combinatorial structures (Latin squares and secret sharing schemes).

Chromatic number:

1. Bounds for the b-chromatic number of some families of graphs (with Mekkia Kouider) Discrete math. 306 (2006) 617-623 Review from MathSciNet.
2. New bounds for the chromatic number of graphs, J. Graph Theory, June (2008) 110-122.
3. On lower bounds for the chromatic number in terms of vertex degree, Discrete Math., 311 (2011) 1365-1370.
4. On (\delta,\chi)-bounded graphs (with Andras Gyarfas), The Electronic Journal of Combinatorics 18 (2011), \#P108.
5. Bounds for chromatic number in terms of even-girth and booksize, Discrete Math. 311 (2011) 197-204.
6. A note on orientation and chromatic number of graphs, J. Combin. Optimization 2016.

Grundy number and First-Fit coloring:

1. Grundy chromatic number of the complement of bipartite graphs , Australas. J. Combinatorics 31 (2005) 325-329.
2. Results on the Grundy chromatic number of graphs, Discrete Math. 306 (2006) 3166-3173 Review from MathSciNet.
3. Inequalities for Grundy chromatic number of graphs, Discrete Applied Math. 155 (2007) 2567-2572 Review from MathSciNet.
4. (\delta, \chi_FF)-bounded families of graphs, Utilitas Mathematica (2016).
5. First-Fit coloring of graphs with no cycles of a prescribed even length, Accepted for publication in J. Combinatorial Optimization (2015).
6. First-Fit coloring of Cartesian product graphs and its defining sets, accepted for publication in Contribution to Discrete Mathematics 2016.
7. More bounds for the Grundy number of graphs (with Z. Tang, B. Wu, L. Hu), accepted for publication in J. Combin. Optim. 2016.

Defining sets and greedy defining sets:

1. Defining sets in vertex coloring of graphs and Latin rectangles (with E.S. Mahmoodian and R. Naserasr) Discrete Math. 167 (1997) 451-460.
2. A characterization of uniquely vertex colorable graphs using defining sets (with H. Hajiabolhassan, M.L. Mehrabadi and R. Tuserkani) Discrete Math. 199 (1999) 233-236.
3. Greedy defining sets of graphs , Australas. J. Combinatorics 23 (2001) 231-235.
4. Greedy defining sets of Latin squares, Ars Combinatoria 89 (2008) 205-222.
5. Greedy defining sets in graphs and Latin squares , Electronic Notes in Discrete Math. 24 (2006) 299-302.
6. More results on greedy defining sets, Ars Combinatoria 114 (2014) 53-64.

Spread of influence in graphs:

1. On dynamic monopolies of graphs with general thresholds, Discrete Math. 312 (2012) 1136--1143.
2. A study of monopolies in graphs (with K. Khoshkhah, M. Nemati, H. Soltani), Graphs and Combinatorics 29 (2013) 1417--1427.
3. On dynamic monopolies of graphs: The strict and average majority thresholds, (with K. Khoshkhah and H. Soltani), Discrete Optimization 9 (2012) 77--83.
4. Dynamic monopolies of directed graphs: The spread of unilateral influence in social networks (with K. Khoshkhah and H. Soltani), Discrete Applied Math. 171 (2014) 81--89.
5. Generalized degeneracy, dynamic monopolies and maximum degenerate subgraphs, Discrete Applied Math. 161 (2013) 2716--2723.
6. Weak dynamic monopolies in graphs (with M. Nemati), Utilitas Mathematica 102 (2017), 113--134.
7. On dynamic monopolies of graphs with probabilistic thresholds (with H. Soltani), B. Australian Mathematical Society, 90 (2014) 363--375.
8. Partial vertex cover and the complexity of some monopoly problems (with H. Soltani), accepted for publication in Utilitas Mathematica (2014).
9. On the largest size of dynamic monopolies with a given average threshold (with K. Khoshkhah), Canadian Mathematical Bulletin, 58 (2015) 306-316.
10. On the size of resistant subgraphs in graphs with average threshold (with M. Nemati), accepted for publication in Utilitas Mathematica (2014)
11. On the monopoly and dynamic monopoly number of Cartesian product of graphs with constant thresholds (with N. Asadi), manuscript (2015).

Independence number:

1. Lower bounds for independence and k-independence number of graphs using the concept of degenerate degree, Discret Applied Math. (2015).

Arrays and Latin squares:

1. Maximum transversal in partial Latin squares and rainbow matchings, Discrete Applied Math. 155 (2007) 558-565.
2. Extending partial \lambda-coloring of graphs with emphasis on K_m\times K_n, Manuscript.
3. Visual cryptography of graph access structures, Manuscript.