Öz
Kaynakça
- 1] M. O. Albertson, The irregularity of a graph, Ars Combin. 46, 219-225, 1997.
Öz
The 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 α (shown in Fig. 1) over all edges of the underlying graph yields, respectively, the second Sombor, symmetric division deg, and inverse symmetric division deg indices. Analogous trigonometric relations for the cosecant and cotangent of α are not possible. Therefore, the only remaining such relation is for the tangent of α, 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.
Anahtar Kelimeler
Teşekkür
The authors would like to present sincere thanks to the editor and the referees. Best regards.
Kaynakça
- 1] M. O. Albertson, The irregularity of a graph, Ars Combin. 46, 219-225, 1997.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Uygulamalı Matematik (Diğer) |
| Bölüm | Matematik |
| Yazarlar | |
| Erken Görünüm Tarihi | 24 Haziran 2025 |
| Yayımlanma Tarihi | |
| Gönderilme Tarihi | 20 Temmuz 2024 |
| Kabul Tarihi | 24 Şubat 2025 |
| Yayımlandığı Sayı | Yıl 2025 Erken Görünüm |