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SOME NODE DEGREE PROPERTIES OF SERIES–PARALLEL GRAPHS EVOLVING UNDER A STOCHASTIC GROWTH MODEL

Published online by Cambridge University Press:  28 March 2013

Hosam M. Mahmoud
Hosam M. Mahmoud*
Affiliation:
Department of Statistics, The George Washington University, Washington, D.C. 20052, U.S.A. E-mail: hosam@gwu.edu
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Abstract

We introduce a natural growth model for directed series-parallel (SP) graphs and look at some of the graph properties under this stochastic model. Specifically, we look at the degrees of certain types of nodes in the random SP graph. We examine the degree of a pole and will find its exact distribution, given by a probability formula with alternating signs. We also prove that, for a fixed value s, the number of nodes of outdegree 1, …, s asymptotically has a joint multivariate normal distribution. Pólya urns will systematically provide a working tool.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 3 , July 2013 , pp. 297 - 307
Copyright
Copyright © Cambridge University Press 2013 

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