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:

Graph theory and combinatorics, in particular chromatic, algorithmic and extremal graph theory, graph modeling of social networks, philosophy of mathematics, typology of mathematicians, mathematical cognition and cognitive scientific approach to mathematical thinking

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.
7. A new vertex coloring heuristic and corresponding chromatic number, submitted.

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, 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.

Dynamic monopolies and 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), Bulletin of Australian Mathematical Society, 90 (2014) 363--375.
8. Partial vertex cover and the complexity of some monopoly problems (with H. Soltani), Utilitas Mathematica (2018).
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 maximum size of resistant subgraphs in graphs with given average threshold (with M. Nemati), Utilitas Mathematica 107 (2018) 251--264.
11. On the monopoly and dynamic monopoly number of Cartesian product of graphs with constant thresholds (with N. Asadi), Ars Combinatoria.
12. On irreversible spread of influence in edge weithed graphs, submitted 2019.
13. Monopolies and dynamic monopolies with constant thresholds of some direct product graphs (with N. Asadi), Ars Combinatoria 2019.

Independence number:

1. Lower bounds for independence and k-independence number of graphs using the concept of degenerate degree, Discrete Applied Math. 203 (2016) 204--216.

Arrays and Latin squares:

1. Maximum transversal in partial Latin squares and rainbow matchings, Discrete Applied Math. 155 (2007) 558-565.
2. More relations between lambda-labeling and Hamiltonian paths with emphasis on line graph of bipartite multigraphs, submitted.
3. Visual cryptography of graph access structures, Manuscript.