Year: 2024
Type: article
Abstract: Let G=(V,E) be a graph. The first Zagreb index of a graph G is defined as ∑u∈VdG2(u), where dG(u) is the degree of vertex u in G. A graph G is called Hamiltonian (resp. traceable) if G has a cycle (resp. path) containing all the vertices of G. Using two established inequalities, in this paper, we present sufficient conditions involving the first Zagreb index for Hamiltonian graphs and traceable graphs. We also present upper bounds for the first Zagreb index of a graph and characterize the graphs achieving the upper bounds.
Source: Mathematics
DOI: 10.3390/math12243902
Author: Rao Li
Institution: University of South Carolina Aiken
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,955
OpenAlex ID: W4405283459