Year: 2025
Type: article
Abstract: Let G = (V, E) be a graph.For a vertex w ∈ V , the degree of w is denoted by d(w).The α-first Zagreb index and the αsecond Zagreb index of G are defined, respectively, as u∈V d α (u) and uv∈E d α (u)d α (v).In the case of the α-first Zagreb index, α is a real number different from 0 and 1; for the α-second Zagreb index, α is a nonzero real number.The α-first and α-second Zagreb indices generalize the classical first and second Zagreb indices, respectively.In this paper, upper bounds are presented for the α-first Zagreb index with α > 1 and the α-second Zagreb index with α > 0.Moreover, sufficient conditions are established, based on either the α-first Zagreb index with α > 1 or the α-second Zagreb index with α > 0, for the existence of certain Hamiltonian properties in a graph.
Author: Rao Li
Institution: University of South Carolina Aiken
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4411366998