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On the second Laplacian spectral moment of a graph

Ying Liu; Yu Qin Sun — 2010

Czechoslovak Mathematical Journal

Kragujevac (M. L. Kragujevac: On the Laplacian energy of a graph, Czech. Math. J. () (2006), 1207–1213) gave the definition of Laplacian energy of a graph $G$ and proved $L E (G) \geq 6 n - 8$ ; 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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