In Chapter 3, we found that Fibonacci and Lucas numbers occur in graph theory, specifically in the study of paraffins and cycloparaffins. We now turn our attention to an additional appearance of Lucas numbers in graph theory, and then to some Fibonacci and Lucas determinants.
22.1 AN APPLICATION TO GRAPH THEORY
In 1975, K.R. Rebman of California State University at Hayward established the occurrence of Lucas numbers in the study of spanning trees of wheel graphs . Before we can present the main result, we need to lay some groundwork in the form of two lemmas and some basic vocabulary.