BILANGAN KROMATIK LOKASI UNTUK GRAF K n K m

Authors

  • Auli Mardhaningsih
  • Zulakmal .

DOI:

https://doi.org/10.25077/jmu.4.1.122-128.2015

Abstract

Misalkan G adalah graf terhubung dan c merupakan pewarnaan k yang sesuai
dari G dengan warna 1; 2; ; k. Misalkan = fS
1
; S
2
; ; S
g adalah partisi V (G)
menjadi kelas-kelas warna yang saling bebas, dimana S
i
k
merupakan himpunan titik
dengan warna i, 1 i k. Kode warna c
(v) dari titik V didenisikan sebagai 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 pewarnaan kromatik lokasi
dari G. Pewarnaan lokasi dengan minimum warna yang digunakan disebut pewarnaan
lokasi minimum. Selanjutnya, kardinalitas dari himpunan yang memuat pewarnaan lokasi
minimum disebut bilangan kromatik lokasi dari G, dinotasikan dengan

(G).
Misalkan terdapat graf G dan H sebarang. Graf korona G 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
i
jV (G)j
, i = 1; 2; 3; ; jV (G)j. Pada tulisan ini akan dikaji kembali makalah [2]
tentang bilangan kromatik lokasi dari graf K
n
K
m
L
, untuk n 1 dan m 1.

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Published

01-03-2015

Issue

Vol. 4 No. 1 (2015)

Section

Articles

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