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On Generalized Fibonacci Numbers of Graphs

In: Applications of Fibonacci Numbers

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  • Michael Drmota

Abstract

A subset I of vertices of a graph G is called independent if no two vertices of I are joined by an edge of G. It is of some interest to determine the number g(G) of independent vertex-sets. For example, consider the graphs Gn with n vertices x1 …,x n such that only the pairs (xi, xi+1), i = 1,…, n − 1, are joined by an edge. It is easy to see that the numbers g n = g(Gn) satisfy the relation $${g_{n + 1}} = {g_n} + {g_{n - 1}}$$ with the initial conditions g1 = 2, g2 = 3. Therefore the numbers g n are essentially the Fibonacci numbers.

Suggested Citation

  • Michael Drmota, 1990. "On Generalized Fibonacci Numbers of Graphs," Springer Books, in: G. E. Bergum & A. N. Philippou & A. F. Horadam (ed.), Applications of Fibonacci Numbers, pages 63-76, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-1910-5_7
    DOI: 10.1007/978-94-009-1910-5_7
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