Ordering of Unicyclic Graphs with Perfect Matchings by Minimal Energies

摘要

The ordering of unicyclic graphs with perfect matchings having 2n vertices according to their minimal energies is considered. Using the method of coefficient comparison and the theorem of zero points, we derive the first 7, 8, 7, 6, and 5 unicyclic graphs with perfect matchings for n ≥ 45, 44 ≥ n ≥ 10, 9≥n≥8,7≥n ≥6, and n = 5,respectively.