SOME PROPERTIES OF BINARY SERIES-PARALLEL GRAPHS. Issue 4 (27th June 2014)

• Record Type: Journal Article
• Authors: Mahmoud, Hosam M.
• Is Part Of: Probability in the engineering and informational sciences. Volume 28:Issue 4(2014)
• Page Start: 565
• Page End: 572
• Publication Date: 2014-06-27
• Subjects: Probabilities -- Periodicals; Engineering -- Statistical methods -- Periodicals; Information science -- Statistical methods -- Periodicals; 519.202462
• DOI: 10.1017/S0269964814000138
• Languages: English
• ISSNs: 0269-9648

Abstract

<abstract abstract-type="normal"> <title> <x content-type="archive" xml:space="preserve">Abstract</x> </title> <p>We introduce an incremental growth model for directed <italic>binary</italic> 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.</p> </abstract>