Topological architecture of derived graphs by means of novel Sombor index
Montes Taurus Journal of Pure and Applied Mathematics, cilt.8, sa.1, ss.140-148, 2026 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 8 Sayı: 1
- Basım Tarihi: 2026
- Dergi Adı: Montes Taurus Journal of Pure and Applied Mathematics
- Derginin Tarandığı İndeksler: Scopus
- Sayfa Sayıları: ss.140-148
- Anahtar Kelimeler: derived graph, Sombor index, topological index
- Bursa Uludağ Üniversitesi Adresli: Evet
Özet
One of the topological graph indices named as Sombor index was defined recently in 2021 by Gutman [12] and received great attention of mathematicians and chemists. For a given graph, derived graphs are the graphs obtained from this graph for several reasons which cannot be concluded by means of the graph itself. Motivated by this popularity of Sombor index, in this work, we determine the Sombor index of some derived graphs such as jump graphs, splitting graphs, r-subdivision graphs, additional vertex and additional edge graphs. Although there are several studies about topological indices of some classical derived graphs, the ones considered here are rather new. We shall also obtain several graph parameters such as the order, size and degree sequence of these derived graphs which can be used in future works related to Sombor index. While the classical methods related to graphs, graph parameters, derived graphs and their known applications are utilized to get the results, one novel technique which is based on recently introduced graph parameter called as omega invariant together with its properties giving cyclomatic number and component number is also used frequently. Also the relations with well-known graph indices are used to establish new identities.