Graph theory and applications

Graph theory meets geometry and topology when researchers assign algebraic quantities—eigenvalues of matrices like the Laplacian, or distance-based indices such as resistance distance and the eccentric connectivity index—to networks and molecular graphs in order to extract structural information that ordinary visual inspection cannot reveal. These spectral and topological descriptors turn abstract connectivity patterns into numbers that predict chemical properties, network robustness, and diffusion behavior, making them valuable tools in both pure mathematics and computational chemistry. Current work centers on sharpening bounds for the spectral radius and Laplacian energy across families of graphs, characterizing which structures extremize a given index, and understanding how distance spectra behave under graph operations like subdivision or coalescing. A deeper open question is whether the full collection of known topological indices can be unified under a common theoretical framework, or whether the diversity of molecular phenomena they capture is irreducibly complex.

Works

46,466

Total citations

405,321

Keywords

Graph SpectraTopological IndicesLaplacian EnergyResistance DistanceMolecular StructureEccentric Connectivity Index