{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T23:00:53Z","timestamp":1769554853782,"version":"3.49.0"},"reference-count":27,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,1]],"date-time":"2024-02-01T00:00:00Z","timestamp":1706745600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A vertex degree based topological index called the Sombor index was recently defined in 2021 by Gutman and has been very popular amongst chemists and mathematicians. We determine the amount of change of the Sombor index when some elements are removed from a graph. This is done for several graph elements, including a vertex, an edge, a cut vertex, a pendant edge, a pendant path, and a bridge in a simple graph. Also, pendant and non-pendant cases are studied. Using the obtained formulae successively, one can find the Sombor index of a large graph by means of the Sombor indices of smaller graphs that are just graphs obtained after removal of some vertices or edges. Sometimes, using iteration, one can manage to obtain a property of a really large graph in terms of the same property of many other subgraphs. Here, the calculations are made for a pendant and non-pendant vertex, a pendant and non-pendant edge, a pendant path, a bridge, a bridge path from a simple graph, and, finally, for a loop and a multiple edge from a non-simple graph. Using these results, the Sombor index of cyclic graphs and tadpole graphs are obtained. Finally, some Nordhaus\u2013Gaddum type results are obtained for the Sombor index.<\/jats:p>","DOI":"10.3390\/sym16020170","type":"journal-article","created":{"date-parts":[[2024,2,1]],"date-time":"2024-02-01T08:44:08Z","timestamp":1706777048000},"page":"170","update-policy":"https:\/\/linproxy.fan.workers.dev:443\/https\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The Effect of Vertex and Edge Removal on Sombor Index"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/linproxy.fan.workers.dev:443\/https\/orcid.org\/0000-0001-8873-1999","authenticated-orcid":false,"given":"Aysun","family":"Yurttas Gunes","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Arts and Science, Bursa Uludag University, Gorukle Campus, Bursa 16059, Turkey"}]},{"ORCID":"https:\/\/linproxy.fan.workers.dev:443\/https\/orcid.org\/0000-0003-1556-3511","authenticated-orcid":false,"given":"Hacer","family":"Ozden Ayna","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Arts and Science, Bursa Uludag University, Gorukle Campus, Bursa 16059, Turkey"}]},{"ORCID":"https:\/\/linproxy.fan.workers.dev:443\/https\/orcid.org\/0000-0002-0700-5774","authenticated-orcid":false,"given":"Ismail Naci","family":"Cangul","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Arts and Science, Bursa Uludag University, Gorukle Campus, Bursa 16059, Turkey"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.30538\/psrp-odam2022.0072","article-title":"Sombor indices-back to geometry","volume":"5","author":"Gutman","year":"2022","journal-title":"Open J. Discret. Appl. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.30538\/psrp-odam2021.0047","article-title":"Some basic properties of Sombor indices","volume":"4","author":"Gutman","year":"2021","journal-title":"Open J. Discret. Appl. Math."},{"key":"ref_3","first-page":"11","article-title":"Geometric approach to degree-based topological indices: Sombor indices","volume":"86","author":"Gutman","year":"2021","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"e26622","DOI":"10.1002\/qua.26622","article-title":"Molecular trees with extremal values of Sombor indices","volume":"121","author":"Deng","year":"2021","journal-title":"Int. J. Quantum Chem."},{"key":"ref_5","first-page":"1","article-title":"Block Sombor index of a graph and its matrix representation","volume":"6","author":"Devaragudi","year":"2023","journal-title":"Open J. Discret. Appl. Math."},{"key":"ref_6","first-page":"703","article-title":"On Sombor index of graphs","volume":"86","author":"Horoldagva","year":"2021","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.14445\/23939133\/IJAC-V8I1P101","article-title":"Computation of Sombor indices of certain networks","volume":"8","author":"Kulli","year":"2021","journal-title":"SSRG Int. J. Appl. Chem."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1007\/s10910-022-01333-y","article-title":"Sombor index: Review of extremal results and bounds","volume":"60","author":"Liu","year":"2022","journal-title":"J. Math. Chem."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"495","DOI":"10.46793\/match.90-2.495L","article-title":"Sombor index of c-cyclic chemical graphs","volume":"90","author":"Liu","year":"2023","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"733","DOI":"10.46793\/match.89-3.733O","article-title":"Mean value of the Sombor index of graphs","volume":"89","author":"Oboudi","year":"2023","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"941","DOI":"10.1007\/s12190-022-01778-z","article-title":"On graphs with integer Sombor index","volume":"69","author":"Oboudi","year":"2023","journal-title":"J. Appl. Math. Comput."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.dam.2021.04.014","article-title":"General properties on Sombor indices","volume":"299","author":"Rada","year":"2021","journal-title":"Discret. Appl. Math."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"451","DOI":"10.46793\/match.89-2.451R","article-title":"On Sombor index and graph energy","volume":"89","author":"Reja","year":"2023","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Unal, S.O. (2022). Sombor index over the tensor and Cartesian product of monogenic semigroup graphs. Symmetry, 14.","DOI":"10.3390\/sym14051071"},{"key":"ref_15","first-page":"715","article-title":"Sombor index of polymers","volume":"86","author":"Alikhani","year":"2021","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1080\/09720510.2022.2043621","article-title":"On Sombor indices of line graph of silicate carbide Si2C3 \u2212 I[p,q]","volume":"25","author":"Asif","year":"2022","journal-title":"J. Discret. Math. Sci. Cryptogr."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Das, K.C., Cevik, A.S., Cangul, I.N., and Shang, Y. (2021). On Sombor Index. Symmetry, 13.","DOI":"10.3390\/sym13010140"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"70","DOI":"10.56557\/jacsi\/2022\/v13i47756","article-title":"Sombor indices of TUAC6 and TUZC6 nanotubes","volume":"13","author":"Divyashree","year":"2022","journal-title":"J. Appl. Chem. Sci. Int."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"e26740","DOI":"10.1002\/qua.26740","article-title":"The expected values of Sombor indices in random hexagonal chains, phenylene chains and Sombor indices of some chemical graphs","volume":"121","author":"Fang","year":"2021","journal-title":"Int. J. Quantum Chem."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"e26689","DOI":"10.1002\/qua.26689","article-title":"More on Sombor indices of chemical graphs and their applications to the boiling point of benzenoid hydrocarbons","volume":"121","author":"Liu","year":"2021","journal-title":"Int. J. Quantum Chem."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"445","DOI":"10.2298\/JSC201215006R","article-title":"Chemical applicability of Sombor indices","volume":"86","year":"2021","journal-title":"J. Serbian Chem. Soc."},{"key":"ref_22","first-page":"91","article-title":"Domination version: Sombor index of graphsand its significance in predicting phsicochemical properties of butane derivatives","volume":"5","author":"Shashidhara","year":"2023","journal-title":"Eurasian Chem. Commun."},{"key":"ref_23","first-page":"91","article-title":"On the modified Sombor indices of some aromatic compounds","volume":"53","author":"Hunag","year":"2021","journal-title":"J. South China Norm. Univ. (Nat. Sci. Ed.)"},{"key":"ref_24","first-page":"1","article-title":"On the product of Sombor and modified Sombor indices","volume":"6","author":"Gutman","year":"2023","journal-title":"Open J. Discret. Appl. Math."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"11263","DOI":"10.3934\/math.2021653","article-title":"Bounds of modified Sombor index, spectral radius and energy","volume":"6","author":"Huang","year":"2021","journal-title":"AIMS Math."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2350098","DOI":"10.1142\/S1793557123500985","article-title":"Modified Sombor index of unicyclic graphs with a given diameter","volume":"16","author":"Shooshtari","year":"2023","journal-title":"Asian-Eur. J. Math."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Zuo, X., Rather, B.A., Imran, M., and Ali, A. (2022). On some topological indices defined via the modified Sombor matrix. Molecules, 27.","DOI":"10.3390\/molecules27196772"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/www.mdpi.com\/2073-8994\/16\/2\/170\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:52:58Z","timestamp":1760104378000},"score":1,"resource":{"primary":{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/www.mdpi.com\/2073-8994\/16\/2\/170"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,1]]},"references-count":27,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2024,2]]}},"alternative-id":["sym16020170"],"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/doi.org\/10.3390\/sym16020170","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,1]]}}}