On energy, Laplacian energy and p-fold graphs - Hilal A Ganie; Shariefuddin Pirzada; Edy Tri Baskoro (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 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)=_i=1^n|λ_i| and the Laplacian energy is defined as LE(G)=_i=1^n|μ_i-2mn|. 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. 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).