2-Distance and 3-Distance Domination Numbers of the Sierpinski Star Graph
- 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.
- Full Text: PDF
- DOI:10.5539/jmr.v16n3p49
Journal Metrics
- h-index (December 2021): 22
- i10-index (December 2021): 78
- h5-index (December 2021): N/A
- h5-median (December 2021): N/A
( The data was calculated based on Google Scholar Citations. Click Here to Learn More. )
Index
- Academic Journals Database
- ACNP
- Aerospace Database
- BASE (Bielefeld Academic Search Engine)
- Civil Engineering Abstracts
- CNKI Scholar
- COPAC
- DTU Library
- EconPapers
- Elektronische Zeitschriftenbibliothek (EZB)
- EuroPub Database
- Google Scholar
- Harvard Library
- IDEAS
- Infotrieve
- JournalTOCs
- LOCKSS
- MathGuide
- MathSciNet
- MIAR
- PKP Open Archives Harvester
- Publons
- RePEc
- ResearchGate
- Scilit
- SHERPA/RoMEO
- SocioRePEc
- Standard Periodical Directory
- Technische Informationsbibliothek (TIB)
- The Keepers Registry
- UCR Library
- Universe Digital Library
- WorldCat
Contact
- Sophia WangEditorial Assistant
- jmr@ccsenet.org