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2-Distance and 3-Distance Domination Numbers of the Sierpinski Star Graph

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  • Khilwa Annida
  • Siti Khabibah
  • Robertus Heri Soelistyo Utomo
  • Lucia Ratnasari

Abstract

The domination set D(G) in graph G=(V(G),E(G)) is a subset of the vertex set in graph G such that every vertex in V(G)\D(G) is adjacent to at least one vertex in D(G). The minimum cardinality of a domination set in graph G is called the domination number and is denoted as γ(G). The set S_k (G) is called the k-distance domination set in graph G if every vertex v in V(G)\S_k (G) has a distance of less than or equal to k from at least one vertex in S_k (G). The minimum cardinality of a k-distance domination set in graph G is called the k-distance domination number and is denoted as γ_k (G). This paper investigated the 2-distance and 3-distance domination sets in the Sierpinski Star graph SS_n and derived the number of 2-distance domination of γ_2 (SS_n)=1 for n<3 and γ_2 (SS_n)=3.3^(n-3) for n≥3, as well as the 3-distance domination number of γ_3 (SS_n)=1 for n<3 and γ_3 (SS_n)=3^(n-3) for n≥3.

Suggested Citation

  • Khilwa Annida & Siti Khabibah & Robertus Heri Soelistyo Utomo & Lucia Ratnasari, 2024. "2-Distance and 3-Distance Domination Numbers of the Sierpinski Star Graph," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 16(3), pages 1-49, December.
    • Handle: RePEc:ibn:jmrjnl:v:16:y:2024:i:3:p:49
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    References listed on IDEAS

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    1. Michael A. Henning & Nicolas Lichiardopol, 2017. "Distance domination in graphs with given minimum and maximum degree," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 545-553, August.
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      JEL classification:

      • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
      • Z0 - Other Special Topics - - General

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