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Distribution of global defensive k-alliances over some graph products

Author

Listed:
  • Mostafa Tavakoli

    (Ferdowsi University of Mashhad)

  • Sandi Klavžar

    (University of Ljubljana
    University of Maribor
    Institute of Mathematics, Physics and Mechanics)

Abstract

If $$G=(V_G, E_G)$$ G = ( V G , E G ) is a graph, then $$S\subseteq V_G$$ S ⊆ V G is a global defensive k-alliance in G if (i) each vertex not in S has a neighbor in S and (ii) each vertex of S has at least k more neighbors inside S than outside of it. The global defensive k-alliance number of G is the minimum cardinality among all global defensive k-alliance in G. In this paper this concept is studied on the generalized hierarchical, the lexicographic, the corona, and the edge corona product. For all of these products upper bounds expressed with related invariants of the factors are given. Sharpness of the bounds is also discussed.

Suggested Citation

  • Mostafa Tavakoli & Sandi Klavžar, 2019. "Distribution of global defensive k-alliances over some graph products," 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. 27(3), pages 615-623, September.
    • Handle: RePEc:spr:cejnor:v:27:y:2019:i:3:d:10.1007_s10100-018-00605-w
    DOI: 10.1007/s10100-018-00605-w
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    Citations

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    Cited by:

    1. Klavžar, Sandi & Tavakoli, Mostafa, 2021. "Dominated and dominator colorings over (edge) corona and hierarchical products," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    2. Andrej Kastrin & Janez Povh & Lidija Zadnik Stirn & Janez Žerovnik, 2021. "Methodologies and applications for resilient global development from the aspect of SDI-SOR special issues of CJOR," 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. 29(3), pages 773-790, September.
    3. Janez Povh & Lidija Zadnik Stirn & Janez Žerovnik, 2019. "Editorial," 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. 27(3), pages 597-599, September.

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