Fibonacci numbers and Lucas numbers in graphs
A subset S?V(G) S ? V ( G ) is independent if no two vertices of S S are adjacent in G G . In this paper we study the number of independent sets in graphs with two elementary cycles. In particular we determine the smallest number and the largest number of these sets among n n -vertex graphs with two elementary cycles. The extremal values of the number of independent sets are described using Fibonacci numbers and Lucas numbers.
fibonacci numbers independent sets counting