The Laplacian energy of random graphs

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• 作者：Wenxue Du ; Xueliang Li ; Yiyang Li
• 关键词：Eigenvalues ; Graph energy ; Laplacian energy ; Random graph ; Random matrices ; Empirical spectral distribution ; Limiting spectral distribution
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2010
• 出版时间：1 August 2010
• 年：2010
• 卷：368
• 期：1
• 页码：311-319
• 全文大小：192 K

文摘

Gutman et al. introduced the concepts of energy and Laplacian energy for a simple graph G, and furthermore, they proposed a conjecture that for every graph G, is not more than . Unfortunately, the conjecture turns out to be incorrect since Liu et al. and Stevanović et al. constructed counterexamples. However, So 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.