Year: 2025
Type: article
Abstract: Let n be a positive integer and f a real function defined on integers in the interval [1, n -1].Given a graph G with vertex set V and n non-isolated vertices, the degree-function index of G is defined as H f (G) = u∈V f (du).It is our main objective in this paper to introduce the local value of a degree-function index H f of a graph G at a vertex u, which we denote by fG (u).Intutively, fG (u) measures the contribution of vertex u in H f (G).In this paper we initiate the study of its mathematical properties and address the problem of vertices with extremal local values in the zeroth-order general Randić index.In particular, for the first Zagreb index and the forgotten index, the problem of vertices with extremal local values is completely solved.
Authors: Instituto de Matem´aticas, Universidad de Antioquia, Colombia, Juan Rada
Institution: Universidad de Antioquia
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4411437868