BILANGAN KROMATIK LOKASI UNTUK GRAF C n K m , DENGAN n 3 DAN m 1

Authors

  • Mery Anggraini
  • Narwen .

DOI:

https://doi.org/10.25077/jmu.4.1.40-46.2015

Abstract

Misalkan G merupakan graf terhubung dan c merupakan pewarnaan k yang
sesuai dari G dengan warna 1; 2; ; k. Misalkan = fS
1
; S
2
; ; S
g merupakan partisi
dari V (G) ke dalam kelas-kelas warna yang saling bebas, dimana S
k
merupakan
himpunan dari titik yang diberi warna i, dengan 1 i k. Kode warna c
(v) dari titik
V merupakan vektor dengan banyak unsur k yaitu
(d(v; S
1
); d(v; S
2
); ; d(v; S
));
dimana d(v; S
i
) adalah jarak dari v ke S
i
k
, dengan 1 i k. Jika untuk setiap dua titik
yang berbeda u; v di G, c

(u) 6 = c
(v), maka c disebut sebagai pewarnaan kromatik
lokasi dari G. Pewarnaan lokasi dengan banyak warna yang digunakan minimum disebut
pewarnaan lokasi minimum, dan kardinalitas dari himpunan yang memuat pewarnaan
lokasi minimum disebut bilangan kromatik lokasi dari G, dinotasikan dengan

(G).
Graf korona G H dari dua graf G dan H adalah graf yang diperoleh
dengan mengambil sebuah duplikat dari graf G dan sebanyak jV (G)j duplikat
H
1
; H
2
; ; H
dari H, kemudian menghubungkan titik ke-i dari graf G ke setiap
titik di H
jV (G)j
, i = 1; 2; 3; ; jV (G)j. Pada tulisan ini, akan dikaji kembali makalah [2]
tentang bilangan kromatik lokasi dari graf C
i
Kata Kunci: Bilangan kromatik lokasi, Graf korona
n

K
m
, n 3 dan m 1.

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Published

01-03-2015

Issue

Vol. 4 No. 1 (2015)

Section

Articles

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