Extremal Graphs with Respect to Matching Energy for Random Six-membered Ring Spiro Chains

Gutman and Wagner (in the matching energy of a graph, Disc. Appl. Math., 2012) defined the matching energy of a graph and pointed out that its chemical applications go back to the 1970s. Now the research on matching energy mainly focuses on graphs with pendent vertices and only a few papers reported the progress on matching energy of graphs without pendent vertices. For a random six-membered ring spiro chain, the number of k -matchings and the matching energy are random variables. In this paper, we determine the extremal graphs with respect to the matching energy for random six-membered ring spiro chains which have no pendent vertices.