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Global Strong Defensive Alliances of Sierpiński-Like Graphs

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Abstract

A strong alliance in a graph G=(V,E) is a set of vertices S⊆V satisfying the condition that, for each v∈S, the number of its neighbors, including itself, in S is greater than the number of those neighbors not in S. A strong alliance S is global if S forms a dominating set of G. In this paper, we shall propose a way for finding a minimum global strong alliance for each of those Sierpiński-like graphs. Furthermore, we also derive the exact values of those global strong alliance numbers.

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Authors and Affiliations

  1. Department of Information Management, National Taiwan University of Science and Technology, Taipei, Taiwan

    Chien-Hung Lin & Yue-Li Wang

  2. Department of Information Management, Shih Hsin University, Taipei, Taiwan

    Jia-Jie Liu

Authors
  1. Chien-Hung Lin
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  2. Jia-Jie Liu
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  3. Yue-Li Wang
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Correspondence to Yue-Li Wang.

Additional information

This work was supported in part by the National Science Council of Republic of China under contracts NSC 100-2221-E-011-067-MY3, NSC 100-2221-E-011-068-, and NSC 100-2221-E-128-003-.

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Lin, CH., Liu, JJ. & Wang, YL. Global Strong Defensive Alliances of Sierpiński-Like Graphs. Theory Comput Syst 53, 365–385 (2013). https://doi.org/10.1007/s00224-012-9423-2

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