Abstract
We introduce an incremental growth model for directed binary series-parallel (SP) graphs. The vertices of a directed binary SP graphs can only have outdgrees 1 or 2. We show that the number of vertices of outdegree 1 have a normal distribution (so, necessarily, the vertices of outdegree 2 have a normal distribution, too). Furthermore, we study the average length of a random walk between the poles of the graph. The asymptotic equivalent of the latter property includes the golden ratio. Pólya urns will systematically provide a coding method to initiate the studies.
Publisher
Cambridge University Press (CUP)
Subject
Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability
Cited by
4 articles.
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1. A SPECTRUM OF SERIES–PARALLEL GRAPHS WITH MULTIPLE EDGE EVOLUTION;Probability in the Engineering and Informational Sciences;2019-01-26
2. Combinatorial Analysis of Growth Models for Series-Parallel Networks;Combinatorics, Probability and Computing;2018-08-14
3. DEGREE PROFILE OF HIERARCHICAL LATTICE NETWORKS;Probability in the Engineering and Informational Sciences;2016-09-13
4. ON THE COMBINATORICS OF BINARY SERIES-PARALLEL GRAPHS;Probability in the Engineering and Informational Sciences;2016-03-09