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Laplacian eigenvalues; Laplacian energy; chromatic number; complement
Kragujevac (M. L. Kragujevac: On the Laplacian energy of a graph, Czech. Math. J. {\it 56}({\it 131}) (2006), 1207--1213) gave the definition of Laplacian energy of a graph $G$ and proved $LE(G)\geq 6n-8$; equality holds if and only if $G=P_n$. In this paper we consider the relation between the Laplacian energy and the chromatic number of a graph $G$ and give an upper bound for the Laplacian energy on a connected graph.
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