Distances in random Apollonian network structures

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dc.creatorBodini, Olivier
dc.creatorDarrasse, Alexis
dc.creatorSoria, Michèle
dc.date2007-12-13
dc.date.accessioned2026-07-07T08:48:59Z
dc.date.available2026-07-07T08:48:59Z
dc.descriptionIn 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 describe the distribution of 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 square root of n.
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/0712.2129
dc.identifierhttp://arxiv.org/abs/0712.2129
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144145
dc.subjectCombinatorics
dc.subject05C12; 05A16
dc.titleDistances in random Apollonian network structures
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