On Irregularity Indices for Fractal and Cayley-Tree Type Dendrimers - Ibraheem, Muhammad; Javaid, Muhammad (Scientific Inquiry and Review, 2025)
Let be a simple connected (molecular) graph with and as the vertex and edge sets respectively. A graph is supposed to be regular if all vertices have equal degree, otherwise irregular. The fractal and cayley trees are irregular acyclic and connected graphs which are widely used to develop signal amplifiers for biosensors, cellular imaging and genetic engineering. The topological index (TI) serves as a mathematical function for determining numerical values of molecular graphs, aiding in the prediction of diverse physical, chemical, biological, thermodynamic, and structural properties. An irregular index, a specific type of TI, quantifies the irregularity of atomic bonding within chemical compounds represented by the graphs under analysis. This study focuses on calculating the irregularity indices for fractal dendrimers and Cayley tree-type dendrimers. A comparative analysis of the obtained indices is conducted using their numerical values and 3D visualizations. Lastly, the most efficient and consistent irregularity indices for fractal and Cayley tree dendrimers are identified and discussed. Keywords:Topological descriptors; Irregularity indices, Fractal dendrimers and Cayley tree dendrimers. MSC (2020) Subject Classification: 05C09; 05C92