DOAJ Open Access 2008

Distances in random Apollonian network structures

Olivier Bodini Alexis Darrasse Michèle Soria

Lihat Sumber DOI

Abstrak

In this paper, we study the distribution of distances in random Apollonian network structures (RANS), a family of graphs which has a one-to-one correspondence with planar ternary trees. Using multivariate generating functions that express all information on distances, and singularity analysis for evaluating the coefficients of these functions, we prove a Rayleigh limit distribution for distances to an outermost vertex, and show that the average value of the distance between any pair of vertices in a RANS of order $n$ is asymptotically $\sqrt{n}$.

Topik & Kata Kunci

Mathematics

Penulis (3)

Olivier Bodini

Alexis Darrasse

Michèle Soria

Format Sitasi

APA MLA BibTeX

Bodini, O., Darrasse, A., Soria, M. (2008). Distances in random Apollonian network structures. https://doi.org/10.46298/dmtcs.3641

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.3641

Informasi Jurnal

Tahun Terbit: 2008
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.3641
Akses: Open Access ✓