On Generalized Fibonacci Numbers of Graphs

Michael Drmota

A chapter in Applications of Fibonacci Numbers, 1990, pp 63-76 from Springer

Abstract: 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.

Date: 1990
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DOI: 10.1007/978-94-009-1910-5_7

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