On $$F_3(k,n)$$-numbers of the Fibonacci type

On the Fibonacci Numbers

The Fibonacci numbers are terms of the sequence defined in a quite simple recursive fashion. However, despite its simplicity, they have some curious properties which are worth attention. In this set of notes, we will look at some of the important features of these numbers. In the first half of the notes, our attention shall be paid to the relationship of the Fibonacci numbers and the Euclidean ...

Energy of Graphs, Matroids and Fibonacci Numbers

The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G. In this article we consider the problem whether generalized Fibonacci constants $varphi_n$ $(ngeq 2)$ can be the energy of graphs. We show that $varphi_n$ cannot be the energy of graphs. Also we prove that all natural powers of $varphi_{2n}$ cannot be the energy of a matroid.

On the Properties of k-Fibonacci Numbers

On the Fibonacci Numbers of Trees

For a graph G, Fibonacci Number of G is defined as the number of subsets of V (G) in which no two vertices are adjacent in G. In this paper, we first investigate the orderings of two classes of trees by their Fibonacci numbers. Using these orderings, we determine the unique tree with the second, and respectively the third smallest Fibonacci number among all trees with n vertices.

On the Euler Function of Fibonacci Numbers

In this paper, we show that for any positive integer k, the set {( φ(Fn+1) φ(Fn) , φ(Fn+2) φ(Fn) , . . . , φ(Fn+k) φ(Fn) )