Exponential Wiener index of some silicate networks

Area of Science:

• Chemistry
• Materials Science
• Graph Theory

Background:

• Topological graph indices, or molecular descriptors, quantify molecular structure for property analysis.
• Silicon and its compounds, silicates, are vital for microelectronics (e.g., PDAs, PCs).
• Understanding silicate properties is key for advancing real-time applications.

Purpose of the Study:

• To introduce and define a novel topological index, the exponential Wiener index.
• To extend this index to include line graphs of silicate molecular structures.
• To compute and analyze this index for specific silicate types.

Main Methods:

• Grouping molecular graph vertices by distance sums to derive the index.
• Applying the exponential Wiener index to cyclic, single-chain, and Pyro silicates.
• Calculating the index for molecular graphs and their line graphs with n=3, 4, 5 vertices.

Main Results:

• The exponential Wiener index was successfully determined for various silicate structures.
• Numerical values for the exponential Wiener index and multiplicative exponential Wiener index were computed.
• The study explored these indices for both original and line graphs of silicates.

Conclusions:

• The exponential Wiener index provides a new tool for analyzing silicate molecular structures.
• This descriptor can offer insights into the physical properties of silicon-based materials.
• The findings contribute to the mathematical characterization of silicates for potential applications.