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.