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Discrete Mathematics & Theoretical Computer Science |
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 $\sqrt{n}$.
Source : ScholeXplorer
IsRelatedTo ARXIV 1509.02129 Source : ScholeXplorer IsRelatedTo DOI 10.1142/s1793830917500276 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1509.02129
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