Wardani, Ayu Anisa and Ratnasari, Lucia and Utomo, Robertus Heri Soelistyo and Khabibah, Siti (2024) Inverse Domination Number and Inverse Total Domination of Sierpinski Star Graph. International Journal of Mathematics and Statistics Studies, 12 (3). pp. 71-79. ISSN 2053-2229 (Print), 2053-2210 (Online)
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Abstract
Given a graph G=(V(G),E(G)) consisting of the set of vertices V(G) and the set of edges E(G). For example, D(G) is a domination set of graph G with minimum cardinality, if V(G)-D(G) contains a domination set D^(-1) (G), then D^(-1) (G) is called the inverse domination set of graph G. The minimum cardinality of the inverse domination set of the graph G is called the inverse domination number, denoted by γ^(-1) (G). If D_t (G) is the total domination set of the graph G with minimal cardinality, and V(G)-D_t (G) contains the total domination set D_t^(-1) (G), then D_t^(-1) (G) is called the inverse total domination set of the graph G. The minimum cardinality of the inverse total domination set of the graph G is called the inverse total domination number, denoted by γ_t^(-1) (G). This paper discusses the inverse domination and the inverse total domination on the Sierpinski Star graph SS_n, obtained the inverse domination number γ^(-1) (SS_n )=0 for n<3 and γ^(-1) (SS_n )=4∙3^(n-3) for n≥3 and the inverse total domination number γ_t^(-1) (SS_n )=0 for n≥1.
| Item Type: | Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Depositing User: | Professor Mark T. Owen |
| Date Deposited: | 07 May 2024 14:23 |
| Last Modified: | 07 May 2024 14:23 |
| URI: | https://tudr.org/id/eprint/2967 |
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