Euler-Sombor index and its congeners
Open Journal of Mathematical Sciences, cilt.9, ss.141-148, 2025 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 9
- Basım Tarihi: 2025
- Doi Numarası: 10.30538/oms2025.0249
- Dergi Adı: Open Journal of Mathematical Sciences
- Derginin Tarandığı İndeksler: Scopus
- Sayfa Sayıları: ss.141-148
- Anahtar Kelimeler: degree (of vertex), Euler-Sombor index, Sombor index, vertex-degree-based graph invariant
- Gazi Üniversitesi Adresli: Evet
Özet
The Euler-Sombor index EU is a vertex-degree-based graph invariant, defined as the sum over all pairs of adjacent vertices u, v of the underlying graph, of the terms (Formula presented) are the degrees of the vertices u and v, respectively. For a real number λ, a variable version of EU is constructed, denoted by EU(λ), defined (Formula presented). Its special cases for λ = 2, −2, 0, and 1 are, respectively, the first Zagreb, Albertson, Sombor, and the ordinary Euler-Sombor indices. The basic properties of EU(λ) are determined, including a method for its approximate calculation and bounds in terms of minimum degree, maximum degree, order and size for several graph products. It is shown how to find values of λ for which EU(λ) is optimal with regard to predicting molecular properties.