On energy, Laplacian energy and $p$-fold graphs - Hilal A Ganie; Shariefuddin Pirzada; Edy Tri Baskoro (Electronic Journal of Graph Theory and Applications (EJGTA), 2015)
For a graph $G$ having adjacency spectrum ($A$-spectrum) $λ_n≤λ_{n-1}≤…≤λ_1$ and Laplacian spectrum ($L$-spectrum) $0=μ_n≤μ_{n-1}≤…≤μ_1$, the energy is defined as $ E(G)=\sum_{i=1}^{n}|λ_i|$ and the Laplacian energy is defined as $LE(G)=\sum_{i=1}^{n}|μ_i-\frac{2m}{n}|$. In this paper, we give upper and lower bounds for the energy of $KK_n^j,~1≤ j ≤ n$ and as a consequence we generalize a result of Stevanovic et al. [More on the relation between Energy and Laplacian energy of graphs, MATCH Commun. Math. Comput. Chem. {\bf 61} (2009) 395-401]. We also consider strong double graph and strong $p$-fold graph to construct some new families of graphs $G$ for which $E(G)> LE(G)$.