Smoothness of Graph Energy in Chemical Graphs

Abstract

The energy of a graph G as a chemical concept leading to HMO theory was introduced by Hückel in 1931 and developed into a mathematical interpretation many years later when Gutman in 1978 gave his famous definition of the graph energy as the sum of the absolute values of the eigenvalues of the adjacency matrix of G. One of the general requirements for any topological index is that similar molecules have close TI values, which is called smoothness. To explore this property, we consider two variants of structure sensitivity and abruptness as introduced by Furtula et al. in 2013 and 2019, for hydrocarbons with up to 20 carbon atoms. Finally, we investigate the relationships between graph energies of acyclic hydrocarbons compared to their cyclic versions.