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

Authors: GWANGYEON LEE

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 $n$th $k$-Lucas numbers. In this paper, we give a new relationship between $g_n^{(k)}$ and $l_n^{(k)}$ and the number of $1$-factors of a bipartite graph.

Keywords: $k$-Fibonacci number, $k$-Lucas number, permanent, $1$-factors

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