On Families of Bipartite Graphs Associated with Sums of Fibonacci and Lucas Numbers

In this paper, we consider the relationships between the sums of the Fibonacci and Lucas numbers and 1-factors of bipartite graphs. 1. Introduction The Fibonacci sequence, fFng ; is de…ned by the recurrence relation, for n > 2 Fn = Fn 1 + Fn 2 where F1 = F2 = 1: The Lucas Sequence, fLng ; is de…ned by the recurrence relation, for n > 2 Ln = Ln 1 + Ln 2 where L1 = 1; L2 = 3: The permanent of an n-square matrix A = (aij) is de…ned by