Forma, Vol. 19 (No. 4), pp. 405-412, 2004
Original Paper

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

Haruo Hosoya

Ochanomizu University, Bunkyo-ku, Tokyo 112-8610, Japan
E-mail address:

(Received February 15, 2005; Accepted March 15, 2005)

Keywords: Perfect Matching, Kekulé Structure, Fibonacci Numbers, Lucas Numbers, Polyomino, Polyhex

Abstract. Several sequences of graphs are introduced whose perfect matching numbers, or Kekulé 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.

[Full text] (PDF 1.6 MB)