Star metric dimension of complete, bipartite, complete bipartite and fan graphs

Artigo2022

Reni Umilasari; Ilham Saifudin; Isnawati Lujeng Lestari

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Resumo

One of the topics in graph theory that is interesting and developed continuously is metric dimension. It has some new variation concepts, such as star metric dimension. The order set of Z={z1,z2,…,zn }⊆V(G) called star resolving set of connected graph G if Z is Star Graph and for every vertex in G has different representation to the set Z. The representation is expressed as the distance d(u,z), it is the shortest path from vertex u to z for every u,z∈V(G). Star basis of a graph is the smallest cardinality of star resolving set. The number of vertex in star basis is called star metric dimension of G which denoted by Sdim(G). The purpose of this article is to determine the characteristic of star metric dimension and the value of star metric dimension of some classes of graphs. The method which is used in this study is library research. Some of the results of this research are complete graph has Sdim(Kn )=n-1, for n≥3, bipartite graph K(2,n) has Sdim (K(2,n) )=n, for n≥3. Besides complete bipartite graph hasn’t star metric dimension or for m,n≥3 or it can said that Sdim (K(m,n) )=0. Another graph, that is Fan graph has Sdim (Fn )=2 for 2≤n≤5 and for n≥6 Sdim (Fn )=(2n+3)/5.

Dados da obra

Tipo: Artigo
Periódico: International Journal of Trends in Mathematics Education Research, v. 5, n. 2, p. 199-205
Editora: IIES Independent
Ano: 2022 (2022-06)
Idioma: en
Palavras-chave: metric dimension; star basis; star metric dimension; star resolving set; complete bipartite
DOI: 10.33122/ijtmer.v5i2.137
ISSN: 2621-8488
Acesso: Acesso aberto
Fontes: DOAJ — Directory of Open Access Journals
Na Biblioteca desde: 01/10/2026 · verificada em 03/10/2026

Como citar

ABNT
UMILASARI, Reni; SAIFUDIN, Ilham; LESTARI, Isnawati Lujeng. Star metric dimension of complete, bipartite, complete bipartite and fan graphs. International Journal of Trends in Mathematics Education Research, v. 5, n. 2, p. 199-205, 2022. DOI: https://doi.org/10.33122/ijtmer.v5i2.137.

APA

Umilasari, R., Saifudin, I., & Lestari, I. L. (2022). Star metric dimension of complete, bipartite, complete bipartite and fan graphs. International Journal of Trends in Mathematics Education Research, 5(2), 199-205. https://doi.org/10.33122/ijtmer.v5i2.137

BibTeX

@article{umilasari2022,
  author = {Umilasari, Reni and Saifudin, Ilham and Lestari, Isnawati Lujeng},
  title = {Star metric dimension of complete, bipartite, complete bipartite and fan graphs},
  year = {2022},
  journal = {International Journal of Trends in Mathematics Education Research},
  volume = {5},
  number = {2},
  pages = {199-205},
  publisher = {IIES Independent},
  doi = {10.33122/ijtmer.v5i2.137},
  language = {en}
}

RIS

TY  - JOUR
AU  - Umilasari, Reni
AU  - Saifudin, Ilham
AU  - Lestari, Isnawati Lujeng
TI  - Star metric dimension of complete, bipartite, complete bipartite and fan graphs
PY  - 2022
JO  - International Journal of Trends in Mathematics Education Research
VL  - 5
IS  - 2
SP  - 199
EP  - 205
DO  - 10.33122/ijtmer.v5i2.137
LA  - en
ER  -

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