Chapter 12
Examples from Graph Theory: An Introduction to the Lucas Numbers
Let us start with some basic ideas from graph theory.
An undirected graph G is made up of a nonempty set V of vertices and a set E (possibly empty) of edges between the vertices in V. For example, in Fig. 12.1 (a), we have 
and E = {uv, vw, vv}, where it is understood, for example, that uv = vu. Here we say that 
, 
are neighbors and u, 
are also neighbors—but u, 
are not neighbors. Also, the edge vv shown in the figure is an example of a loop (at 
).
In Fig. 12.1 (b), we have a second undirected graph—this time 
and E = {uv, vw, ux, xy, yu}. Here the edges ux, xy, and yu constitute a cycle. Since this cycle ...
