Search

The Fibonacci numbers are the numbers defined by the linear recurrence equation, in which each subsequent number is the sum of the previous two. In this paper, we propose Fibonacci networks using Fibonacci numbers. The analytical expressions involving degree distribution, average path length and mean first passage time are obtained. This kind of networks exhibits the small-world characteristic and follows the exponential distribution. Our proposed models would provide the valuable insights into the deterministically delayed growing networks.

On the basis of recursive trees, we propose a new kind of deterministic recursive trees (DRT) with a feature that the initial state of recursive trees is a lattice with an arbitrary number of nodes. In the subsequent evolving step, existing nodes create finite nodes. We obtain analytical formulae for degree distribution and average path length. We also study mean first passage time (MFPT) between two nodes over all pairs, which is used to measure the efficiency of random walks in a network. In addition, we derive an exact formula for the MFPT by using the relationship between random walks and resistance distance in a electronic network.