On energy and laplacian energy of graphs

Let G = (V,E) be a simple graph of order n with m edges. The energy of a graph G, denoted by ε(G), is defined as the sum of the absolute values of all eigenvalues of G. The Laplacian energy of the graph G is defined as (Formula presented), where μ₁, μ₂, …, μ_n−1, μ_{n = 0} are the Laplacian eigenvalues of graph G. In this paper, some lower and upper bounds for ε(G) are presented in terms of number of vertices, number of edges, maximum degree and the first Zagreb index, etc. Moreover, a relation between energy and Laplacian energy of graphs is given.