Sequences of Polyomino and Polyhex Graphs whose Perfect Matching Numbers are Fibonacci or Lucas Numbers: The Golden Family Graphs of a New Category
نویسنده
چکیده
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.
منابع مشابه
Some Graph-Theoretical Aspects of the Golden Ratio: Topological Index, Isomatching Graphs, and Golden Family Graphs
By defining the non-adjacent number, p(G, k), and topological index, ZG, for a graph G, several sequences of graphs are shown to be closely related to the golden ratio, τ. Namely, the Z-values of the path and cycle graphs are Fibonacci, and Lucas numbers, respectively, and thus the ratio of consecutive terms of Z converges to τ. Several new sequences of graphs (golden family graphs) were found ...
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