%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, …, 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