Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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STRONG DOMINATION NUMBER OF GENERALIZED SIERPIŃSKI GRAPHS

  • Manju K. Menon (Department of Mathematics St. Paul's College) ;
  • Gisha Saraswathy (Department of Mathematics Maharaja's College)
  • Received : 2023.08.01
  • Accepted : 2025.08.04
  • Published : 2025.10.31
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Abstract

The generalized Sierpiński graph is a well-known class of interconnection network. Any network can be modeled by a connected graph G = (V, E), where V is the set of nodes and E is the set of the direct communication links between the nodes. Many graph theoretical parameters are useful in the study of the efficiency and reliability of an interconnection network model. Let G = (V, E) be a graph, and u, v ∈ V . Then, u strongly dominates v if (i) uv ∈ E and (ii) d(u) ≥ d(v). A set D ⊆ V is a strong-dominating set (sd-set) of G if every vertex in V \ D is strongly dominated by at least one vertex in D. The strong domination number 𝛾st of G is the cardinality of the smallest sd-set. In this paper, we obtain an upper bound for the strong domination number of the generalized Sierpiński graphs. We obtain a condition for the graphs to attain the bound.

Keywords

Acknowledgement

The first author thanks UGC for sanctioning UGC-JRF under the grant number 995/(CSIR-UGC NET JUNE 2018).

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