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

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, Fp(n  ), and their sums, ∑i=1nFp(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.