Ordering of bicyclic graphs by matching energy

Let G be a simple graph of order n and μ₁, μ₂, ⋯, μ_n be the roots of its matching polynomial. The matching energy is defined as the sum Σⁿ_i=1 /μ_i/, which was introduced by Gutman and Wagner in 2012. For bicyclic graphs of order n, the graphs with the first five smallest matching energies are determined and the graph with the second greatest matching energy is also determined in this paper.