KARAKTERISASI POHON DENGAN BILANGAN DOMINASI-LOKASI-METRIK TIGA

Authors

  • Zulfaneti Zulfaneti Universitas PGRI Sumatera Barat
  • Edy Tri Baskoro Institut Teknologi Bandung
  • Hilda Assiyatun Institut Teknologi Bandung

DOI:

https://doi.org/10.25077/jmua.13.4.340-348.2024

Keywords:

Himpunan dominasi, himpunan pembeda, himpunan dominasi-lokasi- metrik

Abstract

Misalkan G = (V;E) adalah graf sederhana dan terhubung. Untuk suatu himpunan R = fr1; r2; : : : ; rkg V dan v 2 V , representasi titik v terhadap R adalah vektor r(vjR) = (d(v; r1); d(v; r2); : : : ; d(v; rk)) dimana d(v; r) menyatakan jarak titik v dan titik r. Himpunan R disebut himpunan pembeda dari G jika semua titik di G memiliki representasi unik terhadap R. Himpunan D disebut himpunan dominasi dari G jika
setiap titik di G-D bertetangga dengan suatu titik v 2 D. Suatu himpunan dominasi
dan juga merupakan himpunan pembeda disebut himpunan dominasi-lokasi-metrik dari
G. Kardinalitas dari himpunan dominasi-lokasi-metrik minimum dari G disebut bilangan dominasi-lokasi-metrik dari G. Semua graf orde n dengan bilangan dominasi-lokasi-metrik 1, 2, n-2 dan n-3 telah ditentukan secara lengkap. Dalam tulisan ini, kami
mengkarakterisasi semua pohon dengan bilangan-dominasi-lokasi-metrik 3 dan secara
khusus membuktikan bahwa tidak ada pohon dengan bilangan-dominasi-lokasi-metrik
sama dengan dimensi metriknya.

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References

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Published

31-10-2024

How to Cite

Zulfaneti, Z., Baskoro, E. T., & Assiyatun, H. (2024). KARAKTERISASI POHON DENGAN BILANGAN DOMINASI-LOKASI-METRIK TIGA. Jurnal Matematika UNAND, 13(4), 340–348. https://doi.org/10.25077/jmua.13.4.340-348.2024

Issue

Vol. 13 No. 4 (2024)

Section

Articles

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