Statistics of planar graphs viewed from a vertex: A study via labeled trees

Details Statistics of planar graphs viewed from a vertex: A study via labeled trees Statistics of planar graphs viewed from a vertex: A study via labeled trees

2003-07-24

arxiv.org/abs/cond-mat/0307606v1

Nucl.Phys. B675 (2003) 631-660

Physics

Condensed Matter

Statistical Mechanics

36 pages, 15 figures, tex, harvmac, epsf

Scientific paper

10.1016/j.nuclphysb.2003.09.046

We study the statistics of edges and vertices in the vicinity of a reference vertex (origin) within random planar quadrangulations and Eulerian triangulations. Exact generating functions are obtained for theses graphs with fixed numbers of edges and vertices at given geodesic distances from the origin. Our analysis relies on bijections with labeled trees, in which the labels encode the information on the geodesic distance from the origin. In the case of infinitely large graphs, we give in particular explicit formulas for the probabilities that the origin have given numbers of neighboring edges and/or vertices, as well as explicit values for the corresponding moments.

Affiliated with

Also associated with

No associations

Rating

Statistics of planar graphs viewed from a vertex: A study via labeled trees does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Statistics of planar graphs viewed from a vertex: A study via labeled trees, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Statistics of planar graphs viewed from a vertex: A study via labeled trees will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-367550