On Sadhana polynomial of the linear parallelogram P(n,m) of benzenoid graph

Mohammad Reza Farahani


Let G be an arbitrary connected graph and C1, C2,..., Ck be the oposite edges, ops strips of a plane graph G. Then the ops strips form a partition of E(G) and the Omega Ω(G,x) and Sadhana Sd(G,x) polynomials of G are defined as  and  where m(G,c) the number of qoc strips of length c.

In this paper we compute the Sadhana polynomial of an infinite class of the linear parallelogram P(m,n) of benzenoid graph.




N. Trinajstić, Chemical Graph Theory, CRC Press, Boca Raton, FL, 1992.

R. Todeschini and V. Consonni, Handbook of Molecular Descriptors, Wiley-VCH, Weinheim, 2000.

H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 1947. 69, 17-20.

M.V. Diudea, S. Cigher, A. E. Vizitiu, O. Ursu and P.E. John. Croat. Chem. Acta, 2006, 79,. 445.

M. V. Diudea, Omega Polynomial. Carpath. J. Math. 2006 22, 43–47.

P.E. John, A.E. Vizitiu, S. Cigher, and M.V. Diudea, MATCH Commun. Math. Comput. Chem. 2007, 57, 479–484.

M.V. Diudea, S. Cigher and P.E. John. MATCH Commun. Math. Comput. Chem, 2008 60, 237–250.

A.R. Ashrafi, M. Ghorbani, M. Jalali, Indian J. Chem., 47A, 538 (2008)

P.V. Khadikar, D. Mandoli, S. Karmakar, S. Sadhana(Sd), Bioinformatics Ttrends, 1, 51 (2006).

P.V. Khadikar, S. Joshi, A.V. Bajaj, D. Mandloi, Bioorg. Med. Chem. Lett., 14, 1187 (2004).

P.V. Khadikar, S. Singh, M. Jaiswal, D. Mandoli, Bioorg. Med. Chem. Lett., 14, 4795 (2004).

P.V. Khadikar, J. Singh, M. Ingle, J. Math. Chem., 42, 433 (2007).

A.E. Vizitiu, S. Cigher, M.V. Diudea and M.S. Florescu, MATCH Commun. Math. Comput. Chem, 2007 57, 457.

M. Saheli, M. Neamati, A. Ilić and M. V. Diudea. Croat. Chem. Acta. 2010 83(4) 395–401.

A. Bahrani and J. Yazdani. Digest. J. Nanomater. Bios. 2008 3(4), 309-314.

A.R. Ashrafi, M. Ghorbani and M. Jalili. Digest. J. Nanomater. Bios. 2009 4(3), 403–406.

M. Ghorbani. Digest. J. Nanomater. Bios. 2011 6(2), 599-602.

M. Ghorbani and M. Ghazi. Digest. J. Nanomater. Bios. 2010 5(4), 843-849.

M. Ghorbani and M. Jalili. Digest. J. Nanomater. Bios. 2009 4(1), 177 - 182.

J. Yazdani and A. Bahrani. Digest. J. Nanomater. Bios. 2009 4(3), 507-510.

M.V. Diudea, S. Cigher, A.E. Vizitiu, M.S. Florescu and P.E. John, J. Math. Chem. 2009 45 316-329.

M.R. Farahani, K. Kato and M.P. Vlad. Studia Univ. Babes-Bolyai. Chemia 2012 57(3), 177-182.

M.R. Farahani. Acta Chim. Slov. 2012, 59, 965–968.

M.R. Farahani. Journal of Chemica Acta, 2013 2, 43-45.

M.R. Farahani. World Applied Sciences Journal. 2012, 20(9), 1248-1251.

M.R. Farahani. 2013, Submited for publish.

P.V. Khadikar. Iranian Journal of Mathematical Chemistry, 2010, 1(1), 7−42

M. Alaeiyan, R. Mojarad, J. Asadpour. Optoelectron. Adv. Mater.-Rapid Commun. 2011, 5(7), 761 -763.

M. Alaeiyan, and J. Asadpour. Optoelectron. Adv. Mater.-Rapid Commun. 2012, 6(1-2), 191–193.

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