Szeged index

Agrawal et al. have studied the anti-histaminic activity of these 2,3-disubstituted thiazolidin-4-one analogues (Table 9) with graph theoretical indices and discovered the following equation for the activity in terms of the rooted Wiener index (Ww), rooted Szeged index (Szw), molecular redundancy index (MRI), and an indicator variable Ipi (for the p-alkyl of the aryl... 

For acyclic graphs, CJDp = CJAp = WW = Dp SZDp, where WW is the -> hyper-Wiener index. Dp the hyper-distance-path index, and SZDp the - hyper-Szeged index, while for cyclic graphs all these descriptors are different. 

In acyclic graphs, the Harary Cluj-distance index Hqjd coincides with the Harary Wiener index //w and the Harary Szeged index Hsz ( //cid = / w = for... 

In acyclic graphs, the Harary Szeged index //sz coincides with the Harary Wiener index Hvv ( sz = while the corresponding hyper-Harary indices are different (Hsz H v) in cyclic graphs all these indices differ [Diudea et al, 1997f]. 

For acyclic graphs the Szeged index SZD is equal to the -> Wiener index VF, the Cluj-distance index CJD and the - Cluj-detour index CJA SZD = W = CJD = C7A For cyclic graphs, SZD = CJD W CJA. 

For any graphs, the hyper-Szeged index SZDp is different from the other hyperindices. 

Examples of Wiener-type indices are -+ detour index, - Kirchhojf number or quasi-Wiener index, - Szeged index, -> all-path Wiener index, -> edge Wiener index, - hyper-Wiener index, -+ Cluj-distance index, - hyper-Cluj-distance index, -> Cluj-detour index, -> hyper-Cluj-detour index, -> Horary indices, -> hyper-Harary indices, -> detour/Wiener index, and - hyper-distance-path index. 

Chepoi, V. and Klavzar, S. (1997). The Wiener Index and the Szeged Index of Benzenoid Systems in Linear Time. J.Chem.lnf.Comput.Sci., 37,752-755. 

Dobrynin, A.A. and Gutman, I. (1996). On the Szeged Index of Unbranched Catacondensed Benzenoid Molecules. Croat.Chem.Acta, 69,845-856. 

Gutman, I. and Klavzar, S. (1995). An Algorithm for the Calculation of the Szeged Index of Benzenoid Hydrocarbons. J.Chem.Inf.Comput.Sci.,35,1011-1014. 

Gutman, I. and Dobrynin, A.A. (1998b). The Szeged Index - A Success Story. Graph Theory Notes New York, 34,37-44. 

Zerovnik, J. (1999). Szeged Index of Symmetric Graphs. J. Chem.Inf.Comput.ScL, 39,77-80. 

Note that the —> Szeged index SZ. equals the Cluj-distance index C]D for any graph. Moreover, for acyclic graphs, the following relationships hold ... 

In acyclic graphs, the Harary Szeged index Hsz coincides with the Harary Wiener index Hw,... 

For acyclic graphs, the Szeged index SZ is equal to the Wiener index W for any graph, the Szeged index SZ is equal to the Clufdistance index CJD. ... 

The hyper-Szeged index SZp is an extension of the Szeged index, which considers contributions from paths of any length and not only contributions from edges. It is calculated from the path-Szeged matrix as... 

Unsymmetrical, symmetric edge- and hyper-Szeged index for ethylbenzene, respectively. 

To make the Szeged index of compounds with odd member rings to be of comparable magnitude with that of compounds containing even member rings, Randic proposed to calculate the Szeged index by also taking into account contributions from atoms at the same distance from the atoms at both ends of a bond. This led to a novel molecular descriptor, which... 

Calculation of revised Wiener index and Szeged index for l-methyl-2-ethylcyclopentane. 6... 

For vertex- and edge-weighted graphs, the Szeged index was defined as [Ivanciuc and Ivanciuc, 1999 Ivanciuc, 20001]... 

A modified Szeged index, called PI index (Padmakar-Ivan index), was defined as [Khadikar, Kale et al., 2001 Khadikar and Karmarkar, 2001 Ashrafi and Manoochehrian, 2006 Klavzar, 2007]... 

To extend all these classes of generalized Wiener indices to cyclic graphs, these indices can be calculated by using the Szeged index algorithm, as modified by Randic in defining the revised Wiener index, that is, counting 1 /2 all the vertices that are at equal distance from both the vertices on each side of the bond. 

Ivanciuc, O. (2000d) Design of topological indices. Part 15. The Szeged index of vertex- and edge-weighted molecular graphs. Rev Roum. Chim., 45, 895-903. 

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