More geometric studies of vertex-degree-based graph indices-tangent Somb or index

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dc.contributor.authorOz, Mert Sinan
dc.contributor.authorGutman, Ivan
dc.date.accessioned2026-02-08T15:15:51Z
dc.date.available2026-02-08T15:15:51Z
dc.date.issued2025
dc.departmentBursa Teknik Üniversitesi
dc.description.abstractThe representation of an edge of a graph in a 2-dimensional coordinate system (shown in Fig. 1) made it possible to get a geometric interpretation of several earlier proposed vertex-degree-based graph indices. In particular, the sum of sine, cosine, and secant of the angle alpha (shown in Fig. 1) over all edges of the underlying graph yields, respectively, the second Somb or, inverse symmetric division deg, and symmetric division deg indices. Analogous trigonometric relations for the cosecant and cotangent of alpha are not possible. Therefore, the only remaining such relation is for the tangent of alpha, resulting in a new vertex-degree-based topological index, the tangent Sombor index, Tan. In this paper, the basic properties of Tan are established. Connected graphs and trees reaching extremal Tan-values are characterized. Inequalities between Tan and other graph indices are established. The chemical usefulness of Tan in terms of structure sensitivity, abruptness, degeneracy, and correlation with some physicochemical properties of octane isomers and other indices is investigated.
dc.identifier.doi10.15672/hujms.1519536
dc.identifier.endpage2205
dc.identifier.issn2651-477X
dc.identifier.issue6
dc.identifier.scopus2-s2.0-105027520700
dc.identifier.scopusqualityQ2
dc.identifier.startpage2195
dc.identifier.urihttps://doi.org/10.15672/hujms.1519536
dc.identifier.urihttps://hdl.handle.net/20.500.12885/5979
dc.identifier.volume54
dc.identifier.wosWOS:001667371200003
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherHacettepe Univ, Fac Sci
dc.relation.ispartofHacettepe Journal of Mathematics and Statistics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzWOS_KA_20260207
dc.subjecttangent Somb or index
dc.subjectSomb or index
dc.subjecttopological index
dc.titleMore geometric studies of vertex-degree-based graph indices-tangent Somb or index
dc.typeArticle

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