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Algorithmic upper bounds for graph geodetic number

Author

Listed:
  • Ahmad T. Anaqreh

    (University of Szeged)

  • Boglárka G.-Tóth

    (University of Szeged)

  • Tamás Vinkó

    (University of Szeged)

Abstract

Graph theoretical problems based on shortest paths are at the core of research due to their theoretical importance and applicability. This paper deals with the geodetic number which is a global measure for simple connected graphs and it belongs to the path covering problems: what is the minimal-cardinality set of vertices, such that all shortest paths between its elements cover every vertex of the graph. Inspired by the exact 0–1 integer linear programming formalism from the recent literature, we propose new method to obtain upper bounds for the geodetic number in an algorithmic way. The efficiency of these algorithms are demonstrated on a collection of structurally different graphs.

Suggested Citation

  • Ahmad T. Anaqreh & Boglárka G.-Tóth & Tamás Vinkó, 2022. "Algorithmic upper bounds for graph geodetic number," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(4), pages 1221-1237, December.
    • Handle: RePEc:spr:cejnor:v:30:y:2022:i:4:d:10.1007_s10100-021-00760-7
    DOI: 10.1007/s10100-021-00760-7
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    References listed on IDEAS

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    1. Wang, Fu-Hsing & Wang, Yue-Li & Chang, Jou-Ming, 2006. "The lower and upper forcing geodetic numbers of block-cactus graphs," European Journal of Operational Research, Elsevier, vol. 175(1), pages 238-245, November.
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    Cited by:

    1. Munongi, Lucia & Mawila, Daphney, 2023. "Risk factors of orphan and vulnerable children in a children’s home during the COVID-19 pandemic," Children and Youth Services Review, Elsevier, vol. 145(C).

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