In mathematics, the Young–Fibonacci graph and Young–Fibonacci lattice, named after Alfred Young and Leonardo Fibonacci, are two closely related structures involving sequences of the digits 1 and 2. Any digit sequence of this type can be assigned a rank, the sum of its digits: for instance, the rank of 11212 is 1 + 1 + 2 + 1 + 2 = 7. As was already known in ancient India, the number of sequences with a given rank is a Fibonacci number. The Young–Fibonacci lattice is an infinite modular lattice having these digit sequences as its elements, compatible with this rank structure. The Young–Fibonacci graph is the graph of this lattice, and has a vertex for each digit sequence. As the graph of a modular lattice, it is a modular graph.