k-Lucas numbers and associated bipartite graphs Original Research Article

For a positive integer kgreater-or-equal, slanted2, the k-Fibonacci sequence {gn(k)} is defined as: g1(k)=cdots, three dots, centered=gk−2(k)=0, gk−1(k)=gk(k)=1 and for n>kgreater-or-equal, slanted2, gn(k)=gn−1(k)+gn−2(k)+cdots, three dots, centered+gn−k(k). Moreover, the k-Lucas sequence {ln(k)} is defined as ln(k)=gn−1(k)+gn+k−1(k) for ngreater-or-equal, slanted1. In this paper, we consider the relationship between gn(k) and ln(k) and 1-factors of a bipartite graph.