Abstract
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.
Highlights
The method for measuring the effect of a ring on the value of the graph energy is long-time known [31,32,33,34]. It is based on the relation between the values of coefficients of the characteristic polynomial φ( G, λ) of a molecular graph and some of its structural details
Previous investigations of the energy effect of a ring detected an influence of the size of a ring, the size of a molecule, and the ring annelation on its value
The results show that the effect of a ring on the values of the resolvent energy and the Estrada index does not experience any impact from the ring annelation
Summary
Molecular descriptors are quantities that may be regarded as numerical representations of a molecule. There are hundreds of these indices [10], but only a couple of them originate from the eigenvalues obtained from the adjacency matrix of a graph These particular indices are mainly used in modeling the physico–chemical properties of molecules. The second representative of this class of topological molecular descriptors that attracted much attention is the Estrada index It was introduced at the beginning of the XXI century, aiming to model the folding of polypeptide chains. This makes resolvent energy a proper candidate for isomers-distinguishing calculations This topological descriptor exhibited good performance in modeling physico–chemical properties, such as boiling point, heat of formation, and logP of hydrocarbons [24]. A similar type of analysis is performed here, aiming to investigate the influence of a ring in a molecule on the values of the eigenvalue–based topological indices. It will be shown how this methodology can be generalized so to be applicable to other eigenvalue–based topological descriptors
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