{"title":"Sombor指数的TEMO定理","authors":"I. Gutman","doi":"10.30538/psrp-odam2022.0067","DOIUrl":null,"url":null,"abstract":"TEMO = topological effect on molecular orbitals was discovered by Polansky and Zander in 1982, in connection with the eigenvalues of molecular graphs. Eventually, analogous regularities were established for a variety of other topological indices. We now show that a TEMO-type regularity also holds for the Sombor index (\\(SO\\)): For the graphs \\(S\\) and \\(T\\), constructed by connecting a pair of vertex-disjoint graphs by two edges, \\(SO(S) < SO(T)\\) holds. Analogous relations are verified for several other degree-based graph invariants.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"74 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"TEMO theorem for Sombor index\",\"authors\":\"I. Gutman\",\"doi\":\"10.30538/psrp-odam2022.0067\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"TEMO = topological effect on molecular orbitals was discovered by Polansky and Zander in 1982, in connection with the eigenvalues of molecular graphs. Eventually, analogous regularities were established for a variety of other topological indices. We now show that a TEMO-type regularity also holds for the Sombor index (\\\\(SO\\\\)): For the graphs \\\\(S\\\\) and \\\\(T\\\\), constructed by connecting a pair of vertex-disjoint graphs by two edges, \\\\(SO(S) < SO(T)\\\\) holds. Analogous relations are verified for several other degree-based graph invariants.\",\"PeriodicalId\":438929,\"journal\":{\"name\":\"Open Journal of Discrete Applied Mathematics\",\"volume\":\"74 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-04-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Open Journal of Discrete Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.30538/psrp-odam2022.0067\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Open Journal of Discrete Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30538/psrp-odam2022.0067","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
TEMO = topological effect on molecular orbitals was discovered by Polansky and Zander in 1982, in connection with the eigenvalues of molecular graphs. Eventually, analogous regularities were established for a variety of other topological indices. We now show that a TEMO-type regularity also holds for the Sombor index (\(SO\)): For the graphs \(S\) and \(T\), constructed by connecting a pair of vertex-disjoint graphs by two edges, \(SO(S) < SO(T)\) holds. Analogous relations are verified for several other degree-based graph invariants.
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