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On the distribution in a graph process

✍ Scribed by B.R. Handa; S.G. Mohanty

Publisher
Elsevier Science
Year
1984
Tongue
English
Weight
161 KB
Volume
50
Category
Article
ISSN
0012-365X

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✦ Synopsis

Capobianco and Frank [1] have defined a simple graph process recursively as follows:

Let G, be the graph at stage n, n = 1, 2, .... G: consists of a single point. If G, (n = 1, 2,...) is complete, G,Γ·I is formed by adding a point with probability one. Otherwise G,+I is formed from G, either by adding a point with probability p or by inserting a line (i.e., edge) with probability 1-p = q.

Let N, and R, be the number of points and the number of lines respectively of graph G,. Clearly N, + R, = n and R~ = (r~.) if G, is complete. We are interested in deriving the distribution of N,. Denote by ak(n) the probability that Nn = k. It is shown by Capobianco and Frank that for k t> 1 and n ~> 1, a~(k) satisfies the following recurrence relations: ak-l(n-1)+ qak(n-1)

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