Extremal values of matching energies of one class of graphs

In 1978, Gutman proposed the concept of graph energy, defined as the sum of the absolute values of eigenvalues of the adjacency matrix of a molecular graph, which is related to the energy of π-electrons in conjugated hydrocarbons. Recently, Gutman and Wagner proposed the concept of matching energy and pointed out that the chemical applications of matching energy go back to the 1970s. In this paper, we study the extremal values of the matching energy and characterize the graphs with minimal matching energy among all tricyclic graphs with a given diameter. Our methods can help to find more extremal values for other classes of molecular networks and the results suggest the structures with extremal energies.