On the growth of bounded trees

Abstract

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.

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

References in corpus (1)

• Statistical mechanics of complex networks

Cited by in corpus (2)

• The spectral dimension of random trees
• The statistical geometry of scale-free random trees