Alikhani, S., Jafari, F. (2013). On the unimodality of independence polynomial of certain classes of graphs. Transactions on Combinatorics, 2(3), 33-41.

Saeid Alikhani; Fatemeh Jafari. "On the unimodality of independence polynomial of certain classes of graphs". Transactions on Combinatorics, 2, 3, 2013, 33-41.

Alikhani, S., Jafari, F. (2013). 'On the unimodality of independence polynomial of certain classes of graphs', Transactions on Combinatorics, 2(3), pp. 33-41.

Alikhani, S., Jafari, F. On the unimodality of independence polynomial of certain classes of graphs. Transactions on Combinatorics, 2013; 2(3): 33-41.

On the unimodality of independence polynomial of certain classes of graphs

The independence polynomial of a graph $G$ is the polynomial $\sum i_kx^k$, where $i_k$ denote the number of independent sets of cardinality $k$ in $G$. In this paper we study unimodality problem for the independence polynomial of certain classes of graphs.

S. Alikhani (2009). Dominating sets and domination polynomials of
graphs. Ph. D. Thesis, Universiti Putra Malaysia.

2

S. Alikhani and Y. H. Peng Introduction to domination polynomial of a graph. Ars Combin., in press,
{http://arxiv.org/abs/0905.2251}..

3

S. Alikhani and F. Jafari (2012). On the independent sets of some nano-structures. Optoelectronics and advanced materials-rapid communications. 6 (9-10), 911-913

4

Y. Bai, B. Zhao and P. Zhao (2009). Extremal Merrifield-Simmons index and Hosoya index of polyphenyl chains. MATCH Commun. Math. Comput. Chem.. 62, 649-656

5

S. Barnard and J. F. Child (1955). Higher Algebra. Macmillan, London.

6

F. Brenti (1994). Log-concave and unimodal sequences in algebra,
combinatorics, and geometry: an update. Contemp. Math.. 178, 417-441

7

R. A. Brualdi (1992). ntroductory combinatorics. Second edition. North-Holland Publishing Co., New York.

8

T. Dov{s}li'{c} and F. M.{a}lo{}y (2010). Chain hexagonal cacti: Matchings and independent sets. Discrete Math.. 310 (12), 1676-1690

9

C. Hoede and X. Li (1994). Clique polynomials and independent set polynomials of graphs. Discrete Math.. 25, 219-228

10

V. E. Levit and E. Mandrescu (2002). On well-covered trees with unimodal independence polynomials. Proceedings of the Thirty-third Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 2002)., Congr. Numer.. 159, 193-202

11

V. E. Levit and E. Mandrescu (2004). Graph products with log-concave independence polynomials. WSEAS Trans. Math.. 3, 487-492

12

V. E. Levit and E. Mandrescu (2004). Very well-covered graphs with log-concave independence polynomials. Carpathian J. Math.. 20, 73-80

13

V. E. Levit and E. Mandrescu (2005). The independence polynomial of a graph—a survey. in: Proceedings of the 1st International Conference on Algebraic Informatics, Aristotle Univ. Thessaloniki, Thessaloniki. , 233-254

14

V. E. Levit and E. Mandrescu (2006). Independence polynomials of well-covered graphs: generic counterexamples for the unimodality conjecture. European J. Combin.. 27, 931-939

15

V. E. Levit and E. Mandrescu (2006). Partial unimodality for independence polynomials of K"{o}nig-Egerváry graphs. Proceedings of the Thirty-Seventh Southeastern International Conference on Combinatorics, Graph Theory and Computing, Congr. Numer.. 179, 109-119

16

V. E. Levit and E. Mandrescu (2007). A family of graphs whose independence polynomials are both palindromic and unimodal. Carpathian J. Math.. 23, 108-116

17

R. C. Read (1968). An introduction to chromatic polynomials. J. Combinatorial Theory. 4, 52-71

18

R. P. Stanley (1989). Log-concave and unimodal sequences in algebra, combinatorics and geometry. Ann. New York Acad. Sci.. 576, 500-535

19

Y. Wang and B. X. Zhu (2011). On the unimodality of independence
polynomials of some graphs. European J. Combin.. 32, 10-20