%0 Journal Article %T Ordering of Unicyclic Graphs with Perfect Matchings by Minimal Matching Energies %A Jianming Zhu %J Open Journal of Discrete Mathematics %P 17-32 %@ 2161-7643 %D 2019 %I Scientific Research Publishing %R 10.4236/ojdm.2019.91004 %X In 2012, Gutman and Wagner proposed the concept of the matching energy of a graph and pointed out that its chemical applications can go back to the 1970s. The matching energy of a graph is defined as the sum of the absolute values of the zeros of its matching polynomial. Let u and v be the non-isolated vertices of the graphs G and H with the same order, respectively. Let w<sub>i</sub> be a non-isolated vertex of graph G<sub>i</sub> where i=1, 2, &#8230;, k. We use G<sub>u</sub>(k) (respectively, H<sub>v</sub>(k)) to denote the graph which is the coalescence of G (respectively, H