Random walks on Fibonacci treelike models

In this paper, we propose a class of growth models, named Fibonacci trees F(t), with respect to the nature of Fibonacci sequence {Ft}. First, we show that models F(t) have power-law degree distribution with exponent greater than 3. Then, we analytically study two significant topological indices, i.e., optimal mean first-passage time (OMFPT) and mean first-passage time (MFPT), for random walks on Fibonacci trees F(t), and obtain the analytical expressions using some combinatorial approaches. The methods used are widely applied for other network models with self-similar feature to derive analytical solution to OMFPT or MFPT, and we select a candidate model to validate this viewpoint. In addition, we observe from theoretical analysis and numerical simulation that the scaling of MFPT is linearly correlated with vertex number of models F(t), and show that Fibonacci trees F(t) possess more optimal topological structure than the classic scale-free tree networks.