On edge detour index polynomials

Subject Areas : Difference and functional equations

Sh. Safari Sabet ¹ , M. Farmani ² , O. Khormali ³ , A. Mahmiani ⁴ , Z. Bagheri ⁵

1 - Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran
2 - Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran
3 - Mathematics and Informatics Research Group, ACECR, Tarbiat Modares University, P. O. Box: 14115-343, Tehran, Iran
4 - Department of Mathematics, Payame Noor University, 19395-4797, Tehran, Iran
5 - Islamic Azad University Branch of Azadshaher, Azadshaher, Iran

Received: 2013-01-01 Accepted : 2013-01-01 Published : 2013-06-01

Keywords: Linear equations system, Heun equation, Wiener process, Stochastic Differential Equation,

Abstract :

The edge detour index polynomials were recently introduced for computing theedge detour indices. In this paper we find relations among edge detour polynomials for the2-dimensional graph of $TUC_4C_8(S)$ in a Euclidean plane and $TUC4C8(S)$ nanotorus.

References:

[1] H. Wiener, Structural determination of paran boiling points, J. Am. Chem. Soc., 69 (1997) 17-20.
[2] A. A. Dobrynin, R. Entringer and I. Gutman, Wiener index for trees: theory and applications, Acta Appl. Math., 66 (3) (2001) 211-249.
[3] F. Harary, Graph Theory, Addison-Wesley, Reading, Massachusetts, 1969.
[4] M. V. Diudea, G. Katona, I. Lukovitz and N. Trinajstic, Detour and Cluj-Detour Indices, Croat. Chem. Acta, 71 (1998) 459-471.
[5] P. E. John, Ueber die Berechnung des Wiener index fuerausgewaehlte Delta-dimensionale Gitterstrukturen, MATCH Commun. Math. Comput. Chem., 32 (1995) 207-219.
[6] R. Jalal Shahkoohi, O. Khormali and A. Mahmiani, The polynomial of detour index for a graph, World Applied Sciences Journal, 15 (10) (2011) 1473-1483.
[7] A. Mahmiani, O. Khormali and A. Iranmanesh, The edge versions of detour index, MATCH Commun. Math. Comput. Chem., 62 (2) (2009) 419-431.
[8] Sh. Safari Sabet, A. Mahmiani, O. Khormali, M. Farmani and Z. Bagheri, On the edge detour index polynomials, Middle-East Journal of Scientic Research, 10 (4) (2011) 539-548.
[9] Sh. Safari Sabet, M. Farmani, O. Khormali, A. Mahmiani and Z. Bagheri, Relations among the edge detour index polynomials in nanotubes, Journal of Mathematical Nanoscience, 3 (1) (2013) 3-12.