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arXiv · 0906.4636

The Laplacian energy of random graphs

Wenxue Du·Xueliang Li·Yiyang Li
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Abstract

Gutman {\it et al.} introduced the concepts of energy $\En(G)$ and Laplacian energy $\EnL(G)$ for a simple graph $G$, and furthermore, they proposed a conjecture that for every graph $G$, $\En(G)$ is not more than $\EnL(G)$. Unfortunately, the conjecture turns out to be incorrect since Liu {\it et al.} and Stevanović {\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.

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Wenxue Du, Xueliang Li, Yiyang Li. 2009-10-10. The Laplacian energy of random graphs. https://arxiv.org/abs/0906.4636

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