Hosoya Matrices as the Numerical Realization of Graphical Matrices and Derived Structural Descriptors

Graphical matrices are used to generate the Hosoya matrices which in turn produce the Hosoya-Wiener indices. The computer program to generate graphical matrices of acyclic structures, the corresponding numerical matrices and double invariants is delineated

GTI-space : the space of generalized topological indices

A new extension of the generalized topological indices (GTI) approach is carried out torepresent 'simple' and 'composite' topological indices (TIs) in an unified way. Thisapproach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randićconnectivity indices are expressed by means of the same GTI representation introduced for composite TIs such as hyper-Wiener, molecular topological index (MTI), Gutman index andreverse MTI. Using GTI-space approach we easily identify mathematical relations between some composite and simple indices, such as the relationship between hyper-Wiener and Wiener index and the relation between MTI and first Zagreb index. The relation of the GTI space with the sub-structural cluster expansion of property/activity is also analysed and some routes for the applications of this approach to QSPR/QSAR are also given

Primjene teorije grafova: topologijski modeli za predvi|anje CDK-1 inhibicijske aktivnosti aloizina

Relationship between the topological indices and cyclin-dependent kinase-1 (CDK-1/cyclin B) inhibitory activity of 6-phenyl[5H]pyrrolo[2,3-b]pyrazines (aloisines) was investigated. Three topological indices – the Wiener Index, a distance-based topological descriptor, the Zagreb group parameter, an adjacency based topological descriptor, and the eccentric connectivity index, an adjacency-cum-distance based topological descriptor were used in the study. A data set comprising 51 analogues of aloisine was selected for the present study. Values of the Wiener index, the Zagreb group parameter and the eccentric connectivity index for each of the 51 analogues included in the data set were computed using an in-house computer program. Resultant data was analyzed and suitable models were developed after identification of active ranges. A biological activity was then assigned to each compound using these models, which was then compared with the reported CDK-1 inhibitory activity. Accuracy of prediction using these models was found to vary from a minimum of ≈82 % to a maximum of 84 %. .Istraživan je odnos izmđ|u topologijskih indeksa i CDK-1 inhibicijske aktivnosti 5-fenil[5H]pirolo[2,3-b]- pirazina (aloizina). Upotrebljena su tri topologijska indeksa: Wienerov indeks, zagrebački indeks i ekscentrični indeks povezanosti, koji su izračunani za 51 aloizin. Dobiveni modeli predviđaju inhibijsku aktivnosti aloizina s točnošću od 82–84 %

Primjene teorije grafova: topologijski modeli za predvi|anje CDK-1 inhibicijske aktivnosti aloizina

Relationship between the topological indices and cyclin-dependent kinase-1 (CDK-1/cyclin B) inhibitory activity of 6-phenyl[5H]pyrrolo[2,3-b]pyrazines (aloisines) was investigated. Three topological indices – the Wiener Index, a distance-based topological descriptor, the Zagreb group parameter, an adjacency based topological descriptor, and the eccentric connectivity index, an adjacency-cum-distance based topological descriptor were used in the study. A data set comprising 51 analogues of aloisine was selected for the present study. Values of the Wiener index, the Zagreb group parameter and the eccentric connectivity index for each of the 51 analogues included in the data set were computed using an in-house computer program. Resultant data was analyzed and suitable models were developed after identification of active ranges. A biological activity was then assigned to each compound using these models, which was then compared with the reported CDK-1 inhibitory activity. Accuracy of prediction using these models was found to vary from a minimum of ≈82 % to a maximum of 84 %. .Istraživan je odnos izmđ|u topologijskih indeksa i CDK-1 inhibicijske aktivnosti 5-fenil[5H]pirolo[2,3-b]- pirazina (aloizina). Upotrebljena su tri topologijska indeksa: Wienerov indeks, zagrebački indeks i ekscentrični indeks povezanosti, koji su izračunani za 51 aloizin. Dobiveni modeli predviđaju inhibijsku aktivnosti aloizina s točnošću od 82–84 %

New Polynomial-Based Molecular Descriptors with Low Degeneracy

In this paper, we introduce a novel graph polynomial called the ‘information polynomial’ of a graph. This graph polynomial can be derived by using a probability distribution of the vertex set. By using the zeros of the obtained polynomial, we additionally define some novel spectral descriptors. Compared with those based on computing the ordinary characteristic polynomial of a graph, we perform a numerical study using real chemical databases. We obtain that the novel descriptors do have a high discrimination power

The Wiener Polynomial Derivatives and Other Topological Indices in Chemical Research

Wiener polynomial derivatives and some other information and topological indices are investigated with respect to their discriminating power and property correlating ability