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ON THE COMBINATORICS OF BINARY SERIES-PARALLEL GRAPHS

Published online by Cambridge University Press:  09 March 2016

Micha Hofri ,
Chao Li  and
Hosam Mahmoud
Micha Hofri
Affiliation:
Department of Computer Science, Worcester Polytechnic Institute, Worcester, MA, USA
Chao Li
Affiliation:
Department of Computer Science, Worcester Polytechnic Institute, Worcester, MA, USA
Hosam Mahmoud
Affiliation:
Department of Statistics, The George Washington University, Washington, D.C., USA E-mail: [email protected]
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Abstract

Binary series-parallel (BSP) graphs have applications in transportation modeling, and exhibit interesting combinatorial properties. This work is limited to the second aspect. The BSP graphs of a given size – measured in edges – are enumerated. Under a uniform probability model, we investigate the asymptotic distribution of the order (number of vertices) and the asymptotic average length of a random walk (under different strategies) of large graphs of the same size. The systematic method throughout is to define the graphs, and the features we evaluate by a structural equation (equivalent to a regular expression). The structural equation is translated into an equation for a generating function, which is then analyzed.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 30 , Issue 2 , April 2016 , pp. 244 - 260
Copyright
Copyright © Cambridge University Press 2016 

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