Abstract:The paper deals with some generalizations of Fibonacci and Lucas sequences, arising from powers of paths and cycles, respectively.In the first part of the work we provide a formula for the number of edges of the Hasse diagram of the independent sets of the h th power of a path ordered by inclusion. For h = 1 such a diagram is called a Fibonacci cube, and for h > 1 we obtain a generalization of the Fibonacci cube. Consequently, we derive a generalized notion of Fibonacci sequence, called h-Fibonacci sequence. T… Show more
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