Sequences of Polyomino and Polyhex Graphs whose Perfect Matching Numbers are Fibonacci or Lucas Numbers: The Golden Family Graphs of a New Category

摘要

Several sequences of graphs are introduced whose perfect matching numbers,or Kekule numbers,K(G),are either Fibonacci or Lucas numbers,or their multiples.Since the ratio of the K(G)s of consecutive members converges to the golden ratio,these sequences of graphs belong to another class of golden family graphs.