Geometric Approach to Degree-Based Topological Indices: Cosine-Rule Generalized Sombor Indices
Abstract
Motivated by the classical cosine rule from the trigonometric geometry, a novel generalization of the Sombor index is proposed.The Cosine-Rule Generalized Sombor index CoRSO θ is defined via the expression d(u) 2 + d(v) 2 -2d(u)d(v) cos θ where d(u) and d(v) denote the degrees of adjacent vertices, and cos θ is the cosine modulator of the degree interaction.The recently proposed variable Euler-Sombor topological index EU(λ, G) defined via the expressionwith restricted parameter λ ∈ [-2, 2] is derived from the new index.The functional generalization of the Sombor index is proposed.Mathematical properties of CoRSO θ index are established and its chemical applicability is demonstrated.
Fields of Study & Subjects
Topological and Geometric Data Analysis
Graph theory and applications
Statistical Mechanics and Entropy
Publication details
- Journal / source
- match Communications in Mathematical and in Computer Chemistry
- Publisher
- University Library in Kragujevac
- Volume
- 1
- Issue
- 96
- Pages
- 295–295
- Publication date
- 21 January 2026