On the Fibonacci and Lucas p-numbers, their sums, families of bipartite graphs and permanents of certain matrices

Abstract

In this paper we consider certain generalizations of the well-known Fibonacci and Lucas numbers, the generalized Fibonacci and Lucas p-numbers. We give relationships between the generalized Fibonacci p-numbers, F-p(n), and their sums, Sigma(n)(i=1) F-p(i) and the 1-factors of a class of bipartite graphs. Further we determine certain matrices whose permanents generate the Lucas p-numbers and their sums. (C) 2007 Elsevier Ltd. All rights reserved.