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SOME PROPERTIES OF BINARY SERIES-PARALLEL GRAPHS

Published online by Cambridge University Press:  27 June 2014

Hosam M. Mahmoud
Hosam M. Mahmoud*
Affiliation:
Department of Statistics, The George Washington University, Washington, DC 20052, USA E-mail: hosam@gwu.edu
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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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 28 , Issue 4 , October 2014 , pp. 565 - 572
Copyright
Copyright © Cambridge University Press 2014 

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