Chen, Xiaogen; Xie, Wanwen Energy of a hypercube and its complement. (English) Zbl 1251.05096 Int. J. Algebra 6, No. 13-16, 799-805 (2012). Summary: Let \(\bar Q_n\) denote the complement of \(n\)-dimensional hypercube \(Q_n\), and let \(E(G)\) and \(LE(G)\) denote, respectively, the (ordinary) energy and Laplacian energy of a graph \(G\). We obtain \[ \begin{aligned} LE(Q_n) &= E(Q_n) = 2\lceil\frac{n}{2}\rceil\binom n{\lceil\frac{n}{2}\rceil}\\ \text{and} LE(\bar Q_n) &= E(\bar Q_n) = (n + 1) \binom n{\lceil\frac{n}{2}\rceil} + 2^n - 2^n - 2, \end{aligned} \]where \(n\geq 1\). Cited in 2 Documents MSC: 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) 05C65 Hypergraphs Keywords:graph complement; hypercube; eigenvalues; energy of graph; Laplacian energy of graph PDFBibTeX XMLCite \textit{X. Chen} and \textit{W. Xie}, Int. J. Algebra 6, No. 13--16, 799--805 (2012; Zbl 1251.05096) Full Text: Link