GRAPH-THEORETIC MODELS I
In Chapter 20, we used the Q-matrix to extract some interesting properties of both Fibonacci and Lucas numbers. We will now employ it to construct graph-theoretic models for them, and then explore some of the well-known identities. These models enable us to study Fibonacci and Lucas numbers in a different perspective.
To begin with, recall that
We are now ready for the models.
21.1 A GRAPH-THEORETIC MODEL FOR FIBONACCI NUMBERS
The Q-matrix can geometrically be translated into a connected graph G with two vertices and ; see Figure 21.1. In fact, Q is the adjacency matrix of the graph, where denotes the number of edges from to , and .