Independent subsets of powers of paths, and Fibonacci cubes

Abstract

We provide a formula for the number of edges of the Hasse diagram of the independent subsets of the h-th power of a path ordered by inclusion. For h=1 such a value is the number of edges of a Fibonacci cube. We show that, in general, the number of edges of the diagram is obtained by convolution of a Fibonacci-like sequence with itself.

Preprint submitted to Electronic Notes in Discrete Mathematics

References in corpus (1)

• On the independent subsets of powers of paths and cycles

Cited by in corpus (2)

• Generalized Fibonacci and Lucas cubes arising from powers of paths and cycles
• Investigating independent subsets of graphs, with Mathematica