Graph theory and applications

Spectral graph theory and chemical topology examine how the algebraic properties of a graph — eigenvalues of its adjacency or Laplacian matrix, distance-based indices like resistance distance, and descriptors such as the eccentric connectivity index — encode structural information about networks and molecules. These mathematical tools let researchers predict physical and chemical properties of compounds from their bond graphs alone, bypassing costly experiments, while also characterizing connectivity and robustness in communication or biological networks. Active research is pushing toward sharper bounds on spectral radii and Laplacian energy for particular graph families, and toward understanding precisely which structural features are captured — or missed — by a given topological index. A deeper open question is whether distinct molecular graphs can share enough spectral and topological invariants to be practically indistinguishable, a problem with direct consequences for drug design and network identification.

Works

45,971

Total citations

402,965

Keywords

Graph SpectraTopological IndicesLaplacian EnergyResistance DistanceMolecular StructureEccentric Connectivity Index