The Zagreb Indices and Some Hamiltonian Properties of Graphs

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

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