{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:16:24Z","timestamp":1760235384775,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,8,18]],"date-time":"2021-08-18T00:00:00Z","timestamp":1629244800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004564","name":"Ministarstvo Prosvete, Nauke i Tehnolo\u0161kog Razvoja","doi-asserted-by":"publisher","award":["51-03-9\/2021-14\/200122"],"award-info":[{"award-number":["51-03-9\/2021-14\/200122"]}],"id":[{"id":"10.13039\/501100004564","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The eigenvalues of the characteristic polynomial of a graph are sensitive to its symmetry-related characteristics. Within this study, we have examined three eigenvalue\u2013based 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\u2013chemical 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\u2013based topological indices should give a hunch how physico\u2013chemical 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.<\/jats:p>","DOI":"10.3390\/sym13081515","type":"journal-article","created":{"date-parts":[[2021,8,18]],"date-time":"2021-08-18T22:51:00Z","timestamp":1629327060000},"page":"1515","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Effect of a Ring onto Values of Eigenvalue\u2013Based Molecular Descriptors"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4956-0407","authenticated-orcid":false,"given":"Izudin","family":"Red\u017eepovi\u0107","sequence":"first","affiliation":[{"name":"Department of Chemistry, Faculty of Science, University of Kragujevac, 34000 Kragujevac, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1928-5494","authenticated-orcid":false,"given":"Slavko","family":"Radenkovi\u0107","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Faculty of Science, University of Kragujevac, 34000 Kragujevac, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5056-6892","authenticated-orcid":false,"given":"Boris","family":"Furtula","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Faculty of Science, University of Kragujevac, 34000 Kragujevac, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Todeschini, R., and Consonni, V. (2009). Molecular Descriptors for Chemoinformatics, Wiley\u2013VCH.","DOI":"10.1002\/9783527628766"},{"key":"ref_2","unstructured":"Roy, K. (2017). The use of topological indices in QSAR and QSPR modeling. Advances in QSAR Modeling\u2013Applications in Pharmaceutical, Chemical, Food, Agricultural and Environmental Sciences, Springer."},{"key":"ref_3","first-page":"161","article-title":"Basic concepts and applications of molecular topology to drug design","volume":"Volume 1","author":"Basak","year":"2014","journal-title":"Advances in Mathematical Chemistry and Applications"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Roy, K., Kar, S., and Das, R.N. (2015). A Primer on QSAR\/QSPR Modeling: Fundamental Concepts, Springer.","DOI":"10.1007\/978-3-319-17281-1"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1573","DOI":"10.2174\/0929867013371923","article-title":"Recent advances on the role of topological indices in drug discovery research","volume":"8","author":"Estrada","year":"2001","journal-title":"Curr. Med. Chem."},{"key":"ref_6","first-page":"85","article-title":"From the connectivity index to various Randi\u0107\u2013type descriptors","volume":"80","author":"Ma","year":"2018","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"ref_7","first-page":"461","article-title":"A survey on graphs extremal with respect to distance\u2013based topological indices","volume":"71","author":"Xu","year":"2014","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"ref_8","first-page":"277","article-title":"Research on graph energies in 2019","volume":"84","author":"Gutman","year":"2020","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"ref_9","first-page":"1","article-title":"The energy of graph","volume":"103","author":"Gutman","year":"1978","journal-title":"Ber. Math. Stat. Sekt. Forschungsz. Graz"},{"key":"ref_10","unstructured":"Gutman, I., and Furtula, B. (2019). Energies of Graphs: Survey, Census, Bibliography, Center Res. SANU & Univ. Kragujevac."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Li, X., Shi, Y., and Gutman, I. (2012). Graph Energy, Springer.","DOI":"10.1007\/978-1-4614-4220-2"},{"key":"ref_12","unstructured":"Gutman, I., and Li, X. (2016). Energies of Graphs: Theory and Applications, Univ. Kragujevac."},{"key":"ref_13","first-page":"229","article-title":"Relating total \u03c0-electron energy of benzenoid hydrocarbons with HOMO and LOMO energies","volume":"84","author":"Furtula","year":"2020","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"ref_14","first-page":"377","article-title":"Bounds for energy of matrices and energy of graphs","volume":"84","author":"Oboudi","year":"2020","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"129789","DOI":"10.1016\/j.molstruc.2020.129789","article-title":"Quality testing of spectrum-based valency descriptors for polycyclic aromatic hydrocarbons with applications","volume":"1228","author":"Hayat","year":"2021","journal-title":"J. Mol. Struct."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1016\/S0009-2614(00)00158-5","article-title":"Characterization of 3D molecular structure","volume":"319","author":"Estrada","year":"2000","journal-title":"Chem. Phys. Lett."},{"key":"ref_17","first-page":"37","article-title":"Resolvent energy and Estrada index of benzenoid hydrocarbons","volume":"2020","author":"Furtula","year":"2020","journal-title":"J. Serb. Soc. Comput. Mech."},{"key":"ref_18","unstructured":"Jahanbani, A., Karimi, A.T., and Rodriguez, J. (2020). Results on the Estrada indices of benzenoid hydrocarbons. Polycyc. Arom. Comp., 1\u201318."},{"key":"ref_19","unstructured":"Cvetkovi\u0107, D., and Gutman, I. (2011). The Estrada index: An updated survey. Selected Topics on Applications of Graph Spectra, Math. Inst. SASA."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"056103","DOI":"10.1103\/PhysRevE.71.056103","article-title":"Subgraph centrality in complex networks","volume":"71","author":"Estrada","year":"2005","journal-title":"Phys. Rev. E"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"075003","DOI":"10.1088\/1751-8113\/44\/7\/075003","article-title":"Perturbation results for the Estrada index in weighted networks","volume":"44","author":"Shang","year":"2011","journal-title":"J. Phys. A Math. Theor."},{"key":"ref_22","first-page":"279","article-title":"Resolvent energy of graphs","volume":"75","author":"Gutman","year":"2016","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"312","DOI":"10.17344\/acsi.2019.5520","article-title":"On relationships of eigenvalue\u2013based topological molecular descriptors","volume":"67","author":"Furtula","year":"2020","journal-title":"Acta Chim. Slov."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"975","DOI":"10.1007\/s10822-020-00320-2","article-title":"Predictive potential of eigenvalue\u2013based topological molecular descriptors","volume":"34","author":"Furtula","year":"2020","journal-title":"J. Comput. Aided Mol. Des."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1007\/s10910-020-01202-6","article-title":"Comparative study on structural sensitivity of eigenvalue\u2013based molecular descriptors","volume":"59","author":"Furtula","year":"2021","journal-title":"J. Math. Chem."},{"key":"ref_26","first-page":"453","article-title":"Conjectures on resolvent energy of graphs","volume":"81","author":"Das","year":"2019","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"ref_27","first-page":"635","article-title":"On trees with smallest resolvent energy","volume":"77","author":"Ghebleh","year":"2017","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"ref_28","first-page":"125958","article-title":"Some bounds for the resolvent energy","volume":"397","author":"Ashrafi","year":"2021","journal-title":"Appl. Math. Comput."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1016\/j.jmaa.2016.10.043","article-title":"Some extremal properties of the resolvent energy, Estrada and resolvent Estrada indices of graphs","volume":"447","author":"Zhu","year":"2017","journal-title":"J. Math. Anal. Appl."},{"key":"ref_30","first-page":"385","article-title":"On degeneracy of A-eigenvalue\u2013based molecular descriptors and r-equienergetic","volume":"84","author":"Furtula","year":"2020","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1515\/zna-1977-0104","article-title":"Effect of a ring on the stability of polycyclic conjugated molecules","volume":"32a","author":"Bosanac","year":"1977","journal-title":"Z. Naturforsch."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1809","DOI":"10.1016\/0040-4020(77)84063-5","article-title":"Quantitative approach to H\u00fcckel rule the relations between the cycles of a molecular graph and the thermodynamic stability of a conjugated molecule","volume":"33","author":"Gutman","year":"1977","journal-title":"Tetrahedron"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1055","DOI":"10.1007\/s00706-005-0295-x","article-title":"Cyclic conjugation energy effects in polycyclic \u03c0-electron systems","volume":"136","author":"Gutman","year":"2005","journal-title":"Monats. Chem."},{"key":"ref_34","unstructured":"Stevanovi\u0107 Hedrih, K.R. (2008). Mathematical modeling of chemical phenomena. Advances in Nonlinear Sciences II\u2013Sciences and Applications, Academy of Nonlinear Sciences."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Gutman, I., and Polansky, O.E. (1986). Mathematical Concepts in Organic Chemistry, Springer.","DOI":"10.1515\/9783112570180"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/S0166-1280(97)00287-X","article-title":"Cyclic conjugation in dianions: Effect of cycles on the thermodynamic stability of polycyclic conjugated dianions","volume":"428","author":"Gutman","year":"1998","journal-title":"J. Mol. Struct. (Theochem)"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1007\/s10910-015-0473-y","article-title":"A combined technique for computation of energy-effect of cycles in conjugated molecules","volume":"53","author":"Fatoorehchi","year":"2015","journal-title":"J. Math. Chem."},{"key":"ref_38","unstructured":"Friedman, B. (2013). Complex Roots of Polynomial Equations, HardPress Publishing."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1038\/s41586-020-2649-2","article-title":"Array programming with NumPy","volume":"585","author":"Harris","year":"2020","journal-title":"Nature"},{"key":"ref_40","unstructured":"Varoquaux, G., Vaught, T., and Millman, J. (2008, January 21). Exploring Network Structure, Dynamics, and Function using NetworkX. Proceedings of the 7th Python in Science Conference, Pasadena, CA, USA. Available online: http:\/\/conference.scipy.org\/proceedings\/SciPy2008\/paper_2\/full_text.pdf."},{"key":"ref_41","unstructured":"(2021, June 16). Mpmath: A Python Library for Arbitrary-Precision Floating-Point Arithmetic (Version 0.18). Available online: http:\/\/mpmath.org\/."},{"key":"ref_42","unstructured":"Clar, E. (1972). The Aromatic Sextet, Wiley."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/8\/1515\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:46:10Z","timestamp":1760165170000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/8\/1515"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,18]]},"references-count":42,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2021,8]]}},"alternative-id":["sym13081515"],"URL":"https:\/\/doi.org\/10.3390\/sym13081515","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,8,18]]}}}