TITLE:
The First Zagreb Index, the Independence Number and Some Hamiltonian Properties of Graphs
AUTHORS:
Rao Li
KEYWORDS:
The First Zagreb Index, The Independence Number, Hamiltonian Graph, Traceable Graph
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.15 No.4,
September
5,
2025
ABSTRACT: Let
G=(
V,E
)
be a graph. The first Zagreb index of a graph
G
is defined as
∑
u∈V
d
G
2
(
u
)
, where
d
G
(
u
)
is the degree of vertex
u
in
G
. In this paper, we obtain two lower bounds involving the independence number for the first Zagreb index of a graph. We also characterize the graphs achieving the bounds. We further present sufficient conditions based on the first Zagreb index for Hamiltonian graphs and traceable graphs.