ON COMPUTATION OF NEW DEGREE-BASED TOPOLOGICAL INDICES OF SILICATE CHAIN GRAPH

The Arithmetic-Geometric index (AG1 index), SK index, SK1 index, SK2 indices of a graph G was introduced by V. S. Shigehalli and R. R. Kanabur. These topological indices explain the modeling of various physico-chemical, biological and pharmacological properties of organic molecules in chemistry and explains studies of various results on Silicate Chain Graph.

ON THE INVARIANT OF NEW DEGREE-BASED TOPOLOGICAL INDICES OF SILICATE CHAIN GRAPH

Throughout this paper simple and undirected graphs are considered. Let G = (V,E) be such a graph. The structure of a chemical compound can be represented by a graph whose vertex and edge specify the atom and bonds respectively. In this paper we compute certain topological indices of silicate chain.

Ca3ZnGeO2[Ge4O12]: a Ca–Zn germanate related to the mineral taikanite

The title compound, Ca3ZnGeO2[Ge4O12] (tricalcium zinc germanium dioxide dodecaoxidotetragermanate), adopts a taikanite-type structure. The tetrahedral [Ge4O12] chain geometry is very similar to that of the silicate chain of taikanite,i.e.BaSr2Mn3+2O2[Si4O12], while the major difference is found parallel to thecaxis. In taikanite, Mn3+octahedra form an infinite zigzag chain, whereas the title compound has a chain of distorted ZnO6octahedra, which alternates with distorted GeO4tetrahedra connected to each otherviatwo common edges. Eightfold-coordinated Ca2+polyhedra and ZnO6octahedra form a slab parallel to (001) which alternates with another slab containing the tetrahedrally coordinated Ge sites along thecaxis.

The influence of cation properties on the shape of silicate chains

The shape of silicate single chains is described by their periodicity (number of tetrahedra in the repeat unit of the chain) and the degree of shrinkage compared with a maximum stretched chain.From a regression analysis of 54 single chain silicates it is concluded that such silicates can be divided into two groups: (1) Silicates with odd-periodic chains (pyroxenoids and pyroxenes) and (2) silicates with even-periodic chains.Although the results of the analysis are not accurate enough to make reliable quantitative predictions about the shape of a silicate chain merely from the chemical composition of the silicate, some general relations could be found. So it turned out that even-periodic chains become less stretched with higher mean electronegativity and higher mean valence of their cations. In contrast, for odd-periodic chain silicates the degree of chain shrinkage is strongly correlated with the mean electronegativity and less so with the mean radius of the cations. On the other hand, the periodicity of the silicate chains is directly correlated with their degree of shrinkage. These results of the regression analysis are explained in terms of simple crystal chemical considerations.