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 wi？be a non-isolated
vertex of graph Gi？where i=1, 2, …, k. We use Gu(k)？(respectively, Hv(k)) to denote the graph which is the coalescence of G (respectively, H
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