Effect of a Ring onto Values of Eigenvalue-Based Molecular Descriptors

The eigenvalues of the characteristic polynomial of a graph are sensitive to its symmetry-related characteristics. Within this study, we have examined three eigenvalue-based molecular descriptors. These topological molecular descriptors, among others, are gathering information on the symmetry of a molecular graph. Furthermore, they are being ordinarily employed for predicting physico-chemical properties and/or biological activities of molecules. It has been shown that these indices describe well molecular features that are depending on fine structural details. Therefore, revealing the impact of structural details on the values of the eigenvalue-based topological indices should give a hunch how physico-chemical properties depend on them as well. Here, an effect of a ring in a molecule on the values of the graph energy, Estrada index and the resolvent energy of a graph is examined.