The normalized signless laplacian estrada index of graphs

Abstract

Let $G$ be a simple connected graph of order $n$ with $m$ edges. Denote by $% \gamma _{1}^{+}\geq \gamma _{2}^{+}\geq \cdots \geq \gamma _{n}^{+}\geq 0$ the normalized signless Laplacian eigenvalues of $G$. In this work, we define the normalized signless Laplacian Estrada index of $G$ as $NSEE\left(G\right) =\sum_{i=1}^{n}e^{\gamma _{i}^{+}}.$ Some lower bounds on $%NSEE\left( G\right) $ are also established.

Keywords

• normalized signless laplacian eigenvalues
• topological indices (of graph)
• estrada index (of graph)