IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v358y2019icp449-454.html
   My bibliography  Save this article

The reliability of lexicographic product digraphs

Author

Listed:
  • Liu, Qinghai
  • Hong, Yanmei

Abstract

For two digraphs D=(V1,A1) and H=(V2,A2), the lexicographic product digraph D[H] is the digraph with vertex set V1 × V2. There is an arc from vertex (x1, y1) to vertex (x2, y2) in D[H] if and only if either x1x2 ∈ A1 or x1=x2 and y1y2 ∈ A2. The minimum degree and the arc-connectivity of D are denoted by δ(D) and λ(D), respectively. We prove that for any two digraphs D and H, λ(D[H])≥min{n(t+λ(D)−δ(D)−1)+δ(D[H]),n2λ(D)} holds for any t≤min{δ(D)−λ(D)+1,λ(D)+1,n−1}, where n=|V(H)|. As a consequence, λ(D[H])≥n(λ(D)−δ(D))+δ(D[H]). We also provide some sufficient conditions for D[H] to have maximum reliability with respected the connectedness and super connectedness.

Suggested Citation

  • Liu, Qinghai & Hong, Yanmei, 2019. "The reliability of lexicographic product digraphs," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 449-454.
    • Handle: RePEc:eee:apmaco:v:358:y:2019:i:c:p:449-454
    DOI: 10.1016/j.amc.2019.04.040
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319303285
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.04.040?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wang, Shiying & Ma, Xiaolei, 2018. "The g-extra connectivity and diagnosability of crossed cubes," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 60-66.
    2. Zhao, Shuang & Meng, Jixiang, 2018. "Sufficient conditions for hypergraphs to be maximally edge-connected," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 362-368.
    3. Zhou, Qiannan & Wang, Ligong & Lu, Yong, 2018. "Some sufficient conditions on k-connected graphs," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 332-339.
    4. Liu, Yan & Mei, Jingling & Li, Wenxue, 2018. "Stochastic stabilization problem of complex networks without strong connectedness," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 304-315.
    5. Guo, Litao & Su, Guifu & Lin, Wenshui & Chen, Jinsong, 2018. "Fault tolerance of locally twisted cubes," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 401-406.
    6. Zeng, De-Yan & Yin, Jian-Hua, 2018. "An extremal problem on graphic sequences with a realization containing every ℓ-tree on k vertices," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 487-493.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xu, Liqiong, 2024. "Fault tolerability evaluation for the component edge-connectivity of folded Petersen networks," Applied Mathematics and Computation, Elsevier, vol. 473(C).
    2. Guo, Ying & Li, Yuze, 2022. "Bipartite leader-following synchronization of fractional-order delayed multilayer signed networks by adaptive and impulsive controllers," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    3. Zhang, Guozhen & Wang, Dajin, 2019. "Structure connectivity and substructure connectivity of bubble-sort star graph networks," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    4. Lin, Shangwei & Zhang, Wenli, 2020. "The 1-good-neighbor diagnosability of unidirectional hypercubes under the PMC model," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    5. Balbuena, C. & Marcote, X., 2019. "The p-restricted edge-connectivity of Kneser graphs," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 258-267.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:358:y:2019:i:c:p:449-454. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.