Fibonacci numbers and Lucas numbers in graphs

A subset S⊆V(G)S⊆V(G) is independent if no two vertices of SS are adjacent in GG. 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 nn-vertex graphs with two elementary cycles. The extremal values of the number of independent sets are described using Fibonacci numbers and Lucas numbers.