Shahid Rajaee Teacher Training UniversityJournal of Mathematical Nanoscience2538-231411-220110601Hosoya index and Fibonacci numbers515746310.22061/jmns.2011.463ENSaeidAlikhaniDepartment of Mathematics, Yazd University, 89195-741, Yazd, IranJournal Article20110103Let G =(V ,E) be a simple graph. The Hosoya index Z(G) of G is defined as the total number of edge independent sets of G . Fibonacci numbers are terms of the sequence defined in a quite simple recursive fashion. In this paper, we investigate the relationships between Hosoya index and Fibonacci numbers. Also we consider Fibonacci cubes and study some of its parameters which is related to Fibonacci numbers.http://jmathnano.sru.ac.ir/article_463_950607c0b986bf22dd9266dc3b925575.pdf