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Fibonacci numbers of trees

Startek M., Włoch A., Włoch I.

Journal of Mathematics and Applications

2006

Vol. 28

137-145

In [6] it was presented a graph-representation of the Fibonacci numbers Fn and Lucas numbers Ln. It is interesting to know that they are the totał numbers of independent sets of undirected graphs Pn and Cn, respectively. More general concept of the number of all k-independent sets of graphs Pn and Cn was discussed in [5]. In [6], [7] it was bounded the number of all independent sets of a tree Tn. In this paper we propose the method which estimate the number Fk(Tn) of all k-independent sets of Tn. We also describe graphs G for which the numbers Fk(G) are the generalizations of the Fibonacci numbers.