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 { F t } . 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 ( O M F P T ) and mean first-passage time ( M F P T ), 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 O M F P T or M F P T , and we select a candidate model to validate this viewpoint. In addition, we observe from theoretical analysis and numerical simulation that the scaling of M F P T 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.