Himpunan Pembeda tanpa Titik Terisolasi Graf Kincir (K_1+mK_n)

Authors

  • Wahyuni Abidin Universitas Islam Negeri Alauddin Makassar
  • Muhammad Ridwan Universitas Islam Negeri Alauddin Makassar

DOI:

https://doi.org/10.24252/msa.v13i1.60625

Keywords:

Bilangan pembeda tanpa titik terisolasi, himpunan pembeda tanpa titik terisolasi, graf kincir, graf palm

Abstract

Misalkan G = (V,E) adalah graf terhubung, sederhana, dan berhingga. Misalkan himpunan terurut  W = {w_1, w_2, . . ., w_k}   merupakan subhimpunan dari V. Representasi titik v ϵ V  terhadap W  didefinisikan sebagai r(v|W)=d(v,w_1), d(v, w_2), . . ., d(v,w_k) dengan d(v,w_i) menyatakan jarak v dan w_i. Himpunan W dikatakan himpunan pembeda dari G, jika setiap titik dari G  mempunyai representasi yang berbeda. Suatu v merupakan suatu titik terisolasi, jika tidak ada sisi yang terkait dengan titik v. Himpunan pembeda W disebut himpunan pembeda tanpa titik terisolasi, jika subgraf yang diinduksi <W>  tidak mempunyai titik terisolasi. Suatu himpunan pembeda tanpa titik terisolasi dari  G dengan kardinalitas minimum disebut himpunan-nr dari G. Kardinalitas dari himpunan-nr  disebut bilangan pembeda tanpa titik terisolasi yang dinotasikan dengan nr(G).

Berdasarkan hasil penelitian ini, diperoleh bahwa bilangan pembeda tanpa titik terisolasi dari graf K_1 + mK_n  memenuhi nr(K_1+mK_n) = m+1 untuk n = 2 dan nr(K_1+mK_n) = m(n-1), untuk n >=3.  

References

Abidin, W. (2021): Bilangan Pembeda Tanpa Titik Terisolasi Graf Hasil Operasi Korona dan Hasil Operasi Sisir Titik, Disertasi Program Doktor, InstitutTeknologi Bandung.

Avadayappan, S., Bhuvaneshwari, M. dan Chitra, P. J. B. (2018): Non-isolated resolving number for some splitting graphs, International Journal of Mathematical Combinatorics, 9–18.

Diestel, R. (2005): Graph Theory, Springer Book, New York.

Harary, F. dan Melter, R. A. (1976). On themetric dimension of graph, Ars Combinatoria, 2, 191–195.

Chartrand, G., Eroh, L., Johnson, M. A. dan Oellermann, O. R. (2000): Resolvability in graphs and the metric dimension of a graph, Discrete Applied Mathematics, 105, 99–113.

Chartrand, G. dan Zhang, P. (2003): The theory and application of resolvability in graphs, Congressus Numerantium, 160, 47–68.

Chitra, P. J. B. dan Arumugam, S. (2015): Resolving Sets without Isolated Vertices, Procedia Computer Science, 74, 38–42.

Harary, F. dan Melter, R. A. (1976): On the metric dimension of graph, Ars Combinatoria, 2, 191–195.

Khuller, S., Raghavachari, B. dan Rosenfield, A. (1996): Landmarks in graphs, Discrete Applied Mathematics, 70, 217–229.

Santoso, J and Darmaji. (2018): The partition dimension of cycle books graph, doi :10.1088/1742-6596/974/1/012070.

Sebddot{mathrm{o}}, A. dan Tannier, E. (2004): On metric generators of graphs, Mathematics of Operations Research, 29, 383–393.

Slater, P.J. (1975). Leaves of trees, Proceeding of the 6Th Southeastern Conference on Combinatorics, Graph Theory and Computing, Congressus Numerantium, 14, 549-559.

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Published

2025-06-27

How to Cite

[1]
W. Abidin and Muhammad Ridwan, “Himpunan Pembeda tanpa Titik Terisolasi Graf Kincir (K_1+mK_n)”, MSA, vol. 13, no. 1, pp. 150–154, Jun. 2025.

Issue

Vol. 13 No. 1 (2025): VOLUME 13 NO 1 TAHUN 2025

Section

Artikel

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