The Zagreb Indices and Some Hamiltonian Properties of Graphs

Year 2020, Volume: 2 Issue: 2, 7 - 11, 11.07.2020

Rao Li

Abstract

Let $G = (V, E)$ be a graph. The first Zagreb index and second Zagreb index of $G$ are defined as $\sum_{v \in V}d^2(v)$ and
$\sum_{uv \in E}d(u)d(v)$, respectively.
Using first and second Zagreb indexes of graphs, we in this note present sufficient conditions for some Hamiltonian properties of graphs.

Let $G = (V, E)$ be a graph. The first Zagreb index and second Zagreb index of $G$ are defined as $\sum_{v \in V}d^2(v)$ and $\sum_{uv \in E}d(u)d(v)$, respectively. Using first and second Zagreb indexes of graphs, we in this note present sufficient conditions for some Hamiltonian properties of graphs.

Keywords

The first Zagreb index, , The second Zagreb index

References

• Prof. Sunilkumar M. Hosamani, Department of mathematics, Rani Channamma University, Belgaum, India, e-mail: [e-mail]
• Prof. A. DILEK MADEN, Department of Mathematics, Faculty of Science, Selçuk University, Campus, 42075, Konya, Turkey, phone: [phone]; fax: [phone]; e-mail: [e-mail]