In this work we study edge weights for two specific families of increasing trees, which include binary increasing trees and plane oriented recursive trees as special instances, where plane-oriented recursive trees serve as a combinatorial model of scale-free random trees given by the m = 1 case of the BarabásiAlbert model. An edge e = (k, l), connecting the nodes labeled k and l, respectively, ...

We describe a technique that allows the exact analytical computation of the mean first passage time (MFPT) for infinite families of trees using their recursive properties. The method is based in the relationship between the MFPT and the eigenvalues of the Laplacian matrix of the trees but avoids their explicit computation. We apply this technique to find the MFPT for a family of generalized det...

We summarize several limit results for the profile of random plane-oriented recursive trees. These include the limit distribution of the normalized profile, asymptotic bimodality of the variance, asymptotic approximations of the expected width and the correlation coefficients of two level sizes. We also unveil an unexpected connection between the profile of plane-oriented recursive trees (with ...

Many algorithms have been developed to generate sequences for trees, and a few are to generate trees themselves, i.e., in computer representation. Two new algorithms are presented in this paper to generate k-ary trees in computer representation. One is recursive with constant average time per tree and the other is loopless (non-recursive) with constant time per tree. Both of them are simple and...

Recursive neural networks are a new connec-tionist model recently introduced for processing graphs. Linear recursive networks are a special sub-class where the neurons have linear activation functions. The approximation properties of recursive networks are tightly connected to the possibility of distinguishing the patterns by generating a different internal encoding for each input of the domain...