On the growth of bounded trees

Details On the growth of bounded trees On the growth of bounded trees

2001-12-20

arxiv.org/abs/cond-mat/0112394v1

J. Phys. A 35 (2002) 5147-5163

Physics

Condensed Matter

15 pages, revtex4, 4 eps figures, submitted to Journal of Physics A

Scientific paper

10.1088/0305-4470/35/25/301

Bounded infinite graphs are defined on the basis of natural physical
requirements. When specialized to trees this definition leads to a natural
conjecture that the average connectivity dimension of bounded trees cannot
exceed two. We verify that this bound is saturated by a class of random trees,
in which case we derive also explicit expressions for the growth probabilities.

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