Modified Eccentric Connectivity Polynomial of Circumcoronene Series of Benzenoid Hk
DOI:
https://doi.org/10.24297/jap.v2i1.2102Keywords:
Molecular graph, Circumcoronene Series of benzenoid, Modified Eccentricity Connectivity polynomial.Abstract
Let G=(V,E) be a molecular graph, where V(G) is a non-empty set of vertices/atoms and E(G) is a set of edges/bonds. For vV(G), defined dv be degree of vertex/atom v and S(v)is the sum of the degrees of its neighborhoods. The modified eccentricity connectivity polynomial of a molecular graph G is defined as  where ε(v) is defined as the length of a maximal path connecting v to another vertex of molecular graph G. In this paper we compute this polynomial for a famous molecular graph of Benzenoid family.
Downloads
References
H. Wiener, J. Am. Chem. Soc. 69,17 (1947)
H. Hosoya, Bull. Chem. Soc. Jpn. 44, 2332 (1971).
V. Sharma, R. Goswami, A. K. Madan. J. Chem. Inf. Comput. Sci. 37, (1997) 273.
B. Furtula, A. Graovac, D. Vuki?evi?, Disc. Appl. Math.157, 2828 (2009).
H. Dureja, A. K. Madan, Med. Chem. Res. 16, 331 (2007).
M. Fischermann, A. Homann, D. Rautenbach, L. A. Szekely, L. Volkmann, Discrete Appl. Math. 122, 127 (2002).
S. Gupta, M. Singh, A. K. Madan, J. Math. Anal. Appl. 266, 259 (2002).
S. Sardana, A. K. Madan, MATCH Commun. Math. Comput. Chem. 43, 85 (2001).
H. Saheli, H. Saati, A.R. Asfrafi, Optoelectron. Adv. Mater. – Rapid Commun. 4(6), 896 (2010).
V. Kumar, S. Sardana, A. K. Madan, J. Mol. Model. 10, 399 (2004).
M.R. Farahani. Computing a New Connectivity Index for a Famous Molecular Graph of Benzenoid Family. Journal of Chemica Acta 2 (2013) 26-31.
M.R. Farahani. The Ediz Eccentric Connectivity index and the Total Eccentricity Index of a Benzenoid System. Journal of Chemica Acta 2 (2013) 22-2.
M.R. Farahani. Augmented Eccentric Connectivity Index of Molecular Graph. Int J Chem Model 5(4) (2013), In press.
M. Alaeiyan, R. Mojarad, J. Asadpour. A new method for computing eccentric connectivity polynomial of an infinite family of linear polycene parallelogram benzenod. Optoelectron. Adv. Mater.-Rapid Commun. 2011, 5(7), 761 -763.
M. Alaeiyan, and J. Asadpour. Computing the MEC polynomial of an infinite family of the linear parallelogram P(n,n). Optoelectron. Adv. Mater.-Rapid Commun. 2012, 6(1-2), 191 – 193.
A.R. Ashrafi, M. Ghorbani, Electronic Materials Letters, 6(2), 87 (2010).
M.V. Diudea, Studia Univ. Babes-Bolyai, 4, 3-21, (2003)
P. Zigert, S. Klavžar and I. Gutman. Calculating the hyper-Wiener index of benzenoid hydrocarbons. ACH Models Chem. 137, 83-94, (2000)
S. Klavžar, I. Gutman and B. Mohar. Labeling of Benzenoid Systems which Reflects the Vertex-Distance Relations. J. Chem. Int Comput. Sci. 35, 590-593, (1995)
V. Chepoi S. Klavžar. Distances in benzenoid systems: Further developments. Discrete Math. 192, 27-39, (1998)
A. Soncini, E. Steiner, P.W. Fowler, R.W.A. Havenith, and L.W. Jenneskens. Perimeter Effects on Ring Currents in Polycyclic Aromatic Hydrocarbons: Circumcoronene and Two Hexabenzocoronenes. Chem. Eur. J. 9, 2974-2981, (2003)
M.R. Farahani. Zagreb index, Zagreb Polynomial of Circumcoronene Series of Benzenoid. Advances in Materials and Corrosion. (2013).
M.R. Farahani, Computing a New Version of Atom-Bond Connectivity Index of Circumcoronene Series of Benzenoid Hk by Using the Cut Method. Journal Mathematical NanoScience. 2, (2012). In press.
M.R. Farahani, Computing ?(G,x) and ?(G,x) Polynomials of an Infinite Family of Benzenoid. Acta Chim. Slov. 59, 965–968, (2012).
M.R. Farahani, Omega and Sadhana Polynomials of Circumcoronene Series of Benzenoid. World Applied Sciences Journal. 20(9), 1248-1251, (2012).
M.R. Farahani, K. Kato and M.P. Vlad. Omega Polynomials and Cluj-Ilmenau Index of Circumcoronene Series of Benzenoid. Studia Univ. Babes-Bolyai. 57(3) 177-182, (2012).
M.R. Farahani, On the Schultz polynomial, Modified Schultz polynomial, Hosoya polynomial and Wiener index of circumcoronene series of benzenoid, Journal of Applied Mathematics & Informatics. 31(3) in press, (2013).
M.R. Farahani, Computing Fifth Geometric-Arithmetic Index for Circumcoronene series of benzenoid Hk. Journal of Advances in Chemistry. 3(1) (2013) 143-148.
M.R. Farahani, Computing Atom-Bond Connectivity (ABC4) index for Circumcoronene Series of Benzenoid. Journal of Advances in Chemistry. 2(1), (2013), 68-72.
S. Klavžar. A Bird's Eye View of The Cut Method And A Survey of Its Applications In Chemical Graph Theory. MATCH Commun. Math. Comput. Chem. 60, 255-274, (2008).
P.E. John, P.V. Khadikar and J. Singh. A method of computing the PI index of benzenoid hydrocarbons using orthogonal cuts. J. Math. Chem. 42(1), 27-45, (2007).
Downloads
Published
How to Cite
Issue
Section
License
All articles published in Journal of Advances in Linguistics are licensed under a Creative Commons Attribution 4.0 International License.