Some Interpretations of the Generalized Fibonacci Numbers

Abstract

In this paper we give some new interpretations of the generalized Fibonacci numbers and the generalized Lucas numbers. This interpretation is given with respect to the counting of special subfamilies of the set of n integers. Moreover we have applied these numbers for the graph interpretation of the number of all H-matchings in special graphs, where H is a collection of some connected spanning subgraphs of Kk.