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** Correlation weight local graph invariant **

** Graph invariant atom partitioning **

This is the simplest graph invariant obtained from the -> adjacency matrix A, defined as the number of bonds in the -> molecular graph (7 where multiple bonds are considered as single edges. Bond number is calculated as half the - total adjacency index Ay [Pg.28]

Examples of the global graph invariants are represented by the number and size of cycles, and the total number of chemical elements in a molecule. The number of oxygen and/or nitrogen atoms can be (in the first approximation) a measure of [Pg.339]

The ATS descriptor is a graph invariant describing how the considered property is distributed along the topological structure. In fact, assuming an additive scheme, the ATS descriptor corresponds to a decomposition of the square molecular property O in different atomic contributions [Pg.18]

Optimization of Correlation Weights of Local Graph Invariants [Pg.339]

Basak, S. C., Mills, D., Mumtaz, M. M. Use of graph invariants in the protection of human and ecological health. In Basak, S. C., Balakrishnan, R., Eds., Lecture Notes of the First Indo-US Lecture Series on Discrete Mathematical Chemistry, 2007. [Pg.498]

Diudea, M. V., O. Minailiuc, and A. T. Balaban, Regressive Vertex Degree (New Graph Invariants) and Derived Topological Indices. J. Comput. Chem., 1991 12, 527-535. [Pg.37]

The unique properties of fragment descriptors are related to the fact that (i) any molecular graph invariant i.e., any molecular descriptor or property) [Pg.1]

Lemma Bijective (one-to-one, onto) functions [15] exist between each of the above mentioned sets of graph invariants E,V,H,C- In other words we can write the relation as follows [Pg.260]

Other related molecular descriptors are -+ atomic composition indices, several - information indices and - graph invariants. [Pg.16]

Toropov AA, Schultz TW (2003) Prediction of aquatic toxicity Use of optimization of correlation weights of local graph invariants. J. Chem. Inf. Comput. Sci. 43 560-567. [Pg.350]

Toropov, A.A. Toropova, A.P. QSPR modeling of complex stability by optimization of correlation weights of the hydrogen bond index and the local graph invariants. Russ. J. Coord. Chem. 2002, 28 (12), 877-880. [Pg.357]

Castro EA, Toropov AA, Nesterova AI, Nabiev OM (2004) QSPR modeling aqueous solubility of polychlorinated biphenyls by optimization of correlation weights of local and global graph invariants. CEJC 2 500-523. [Pg.349]

Some molecular descriptors, called - determinant-based descriptors, are calculated as the determinant of a - matrix representation of a molecular structure. Moreover, permanents, short- and long-hafnians, calculated on the topological - distance matrix D, were used as graph invariants by Schultz and called per(D) index, shaf(D) index, lhaf(D) index [Schultz et al, 1992 Schultz and Schultz, 1992]. [Pg.6]

In addition to these, only a limited number of other topological indices of benzenoid molecules have been studied. With a few not too important exceptions, generally valid mathematical results were obtained only for one of them — namely for the Wiener index. Therefore the remaining part of this section is devoted to the Wiener index of benzenoid systems. (Further graph invariants worth mentioning in connection with benzenoids, especially unbranched catacondensed systems, are the Hosoya index [119-121], the Merrifield — Simmons index [122, 123], the modified Hosoya index [38] and the polynomials associated with them.) [Pg.23]

See also in sourсe #XX -- [ Pg.7 ]

** Correlation weight local graph invariant **

** Graph invariant atom partitioning **

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