k-Fibonacci numbers and k-Lucas numbers and associated bipartite graphs

Abstract

In [6], [8] and [10], the authors studied the generalized Fibonacci numbers. Also, in [7], the author found a class of bipartite graphs whose number of 1-factors is the nth k-Lucas numbers. In this paper, we give a new relationship between $g^{(k)}_n and l^{(k)}_n$and the number of 1-factors of a bipartite graph.