Smoothness of Graph Energy in Chemical Graphs

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