Note on the temperature Sombor index

Abstract

Introduction/purpose: The temperature of a vertex of a graph of the order n is defined as d/(n-d), where d is the vertex degree. The temperature variant of the Sombor index is investigated and several of its properties established. Methods: Combinatorial graph theory is applied. Results: Extremal values and bounds for the temperature Sombor index are obtained. Conclusion: The paper contributes to the theory of Sombor-index-like graph invariants.