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The Laplacian energy of random graphs
Gutman {\it et al.} introduced the concepts of energy \En(G) and Laplacian
energy \EnL(G) for a simple graph , and furthermore, they proposed a
conjecture that for every graph , \En(G) is not more than \EnL(G).
Unfortunately, the conjecture turns out to be incorrect since Liu {\it et al.}
and Stevanovi\'c {\it et al.} constructed counterexamples. However, So {\it et
al.} verified the conjecture for bipartite graphs. In the present paper, we
obtain, for a random graph, the lower and upper bounds of the Laplacian energy,
and show that the conjecture is true for almost all graphs.Comment: 14 page
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