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Asymptotic Spectral Distributions of Distance-k Graphs of Star Product Graphs

  • Conference paper
XI Symposium on Probability and Stochastic Processes

Part of the book series: Progress in Probability ((PRPR,volume 69))

Abstract

Let G be a finite connected graph and let G [⋆N, k] be the distance-k graph of the N-fold star power of G. For a fixed k ≥ 1, we show that the large N limit of the spectral distribution of G [⋆N, k] converges to a centered Bernoulli distribution, \(1/2\delta _{-1} + 1/2\delta _{1}\). The proof is based in a fourth moment lemma for convergence to a centered Bernoulli distribution.

T. Gaxiola was supported by Conacyt Master’s Scholarship No. 45710.

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Author information

Authors and Affiliations

  1. Research Center for Mathematics, CIMAT, Aparatado Postal 402, Guanajuato, GTO, 36240, Mexico

    Octavio Arizmendi & Tulio Gaxiola

Authors
  1. Octavio Arizmendi
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  2. Tulio Gaxiola
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Corresponding author

Correspondence to Octavio Arizmendi .

Editor information

Editors and Affiliations

  1. Probabilidad y Estadística, IIMAS UNAM, Mexico

    Ramsés H. Mena

  2. CIMAT, Guanajuato, Mexico

    Juan Carlos Pardo

  3. CIMAT, Guanajuato, Mexico

    Víctor Rivero

  4. Instituto de Matemáticas, UNAM, Mexico

    Gerónimo Uribe Bravo

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Arizmendi, O., Gaxiola, T. (2015). Asymptotic Spectral Distributions of Distance-k Graphs of Star Product Graphs. In: Mena, R., Pardo, J., Rivero, V., Uribe Bravo, G. (eds) XI Symposium on Probability and Stochastic Processes. Progress in Probability, vol 69. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-13984-5_2

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