The Graceful Chromatic Number for Some Particular Classes of Graphs

Mincu, Radu Stefan; Obreja, Camelia; Popa, Alexandru

doi:10.1109/synasc49474.2019.00024

Cited by 7 publications

(6 citation statements)

References 3 publications

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“…Selanjutnya [1] menemukan bilangan kromatik graceful pada keluarga graf unicyclic, yaitu graf tadpole, graf pan, dan graf sun. Selanjutnya [8] tentang bilangan kromatik graceful pada beberapa kelas graf khusus. Selanjutnya [9] yang menemukan bilangan kromatik graceful pada keluarga graf unicyclic, yaitu graf bull, graf net, graf cricket, graf caveman, graf peach, dan graf flowerpot.…”

Section: Pendahuluanunclassified

Pewarnaan Graceful Pada Graf Hasil Operasi Comb Graf Siklus Dan Graf Star

Rudi¹,

Wahab²,

Waluyo³

2023

KDMA

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Section: Pendahuluanunclassified

Pewarnaan Graceful Pada Graf Hasil Operasi Comb Graf Siklus Dan Graf Star

Rudi¹,

Wahab²,

Waluyo³

2023

KDMA

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“…Pewarnaan k-graceful adalah pewarnaan titik dimana f : V (G) → {1, 2, ..., k}, dengan k ≥ 2 yang menginduksi pewarnaan sisi dimana f 0 : E(G) → {1, 2, ..., k − 1} didefinisikan f 0 (uv) = |f (u) − f (v)| [3]. Menurut Mincu dkk (2019) pewarnaan k-graceful dari graf terhubung yang tidak berarah G adalah pewarnaan titik yang menggunakan k warna yang menginduksi pewarnaan sisi, di mana warna untuk sisi (u, v) adalah nilai absolut dari selisih antara warna pada titik yang bersinggungan dengan sisi tersebut [8]. Pewarnaan Nafisa Afwa Sania, Bilangan Kromatik Graceful pada Keluarga Graf Unicyclic, CGANT JMA Vol.…”

Section: Pendahuluanunclassified

“…Selanjutnya Alfarisi, dkk [3] menemukan bilangan kromatik graceful pada keluarga graf unicyclic (graf tadpole, graf pan, dan graf sun). Selanjutnya Mincu, dkk [8] juga telah menemukan bilangan kromatik graceful pada beberapa kelas graf khusus.…”

Section: Pendahuluanunclassified

Bilangan Kromatik Graceful pada Keluarga Graf Unicyclic

Sania

Dafik

Fatahillah

2020

CGANT. JOU. OF MATH. AND APP.

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Suppose $ G $ is a graph, where $ G = \{V (G), E (G) \} $. Graceful coloring is defined by $ c: V (G) \to \{1,2, ..., k \} $ which induces a proper edge coloring $ c': E (G) \to \{1,2, ..., k- 1 \}$ defined by $c'(xy)=|c(x)-c(y)|$, where $ k \geq 2 $, $ k \in N $. Coloring is said to be graceful if these 3 conditions are satisfied, namely the proper vertex color, the proper edge color, and the edge color, which are the absolute difference between the color of the accident vertex. The subgraph $H$ on that graceful coloring is smaller than the $G$. Furthermore, one of the subgraphs in the unicyclic graph family is a cycle graph. The graceful chromatic number on a graph denoted by $ \chi_g (G) $, is the optimum number of graceful colors from graph $G$. This research aims to find graceful chromatic numbers in the unicyclic graph family, namely bull graphs, net graphs, cricket graphs, caveman graphs, peach graphs, and flowerpot graphs. The results of this study indicate that $\chi_g(C_l) \geq 4$, where $C_l$ is a unicyclic graphs.

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“…The least k for which a graph G has a graceful k-coloring is called a graceful chromatic number of a graph G, denoted by χ g (G) in [4]. More study of graceful coloring some graphs in [2,8,10,12,13].…”

Section: Introductionmentioning

confidence: 99%

On graceful chromatic number of some graphs

Dafik

Agustin

Nisviasari

et al. 2022

J. Phys.: Conf. Ser.

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We examine that all graphs in this paper are limited, simple and connected. A graceful k-coloring of a graph is a proper vertex coloring f 1 : V (G) → {1, 2,…, k} where k ≥ 2 which induces a proper edge coloring f 2 : E (G) → {1, 2,…, k − 1} characterized by f 2(uυ) = |f 1(u) — f 2 (υ)|. Nethermost k for which a graph G has a graceful k-coloring is named a graceful chromatic number of a graph G, denoted by χg (G). In our research, we will obtain the exact value of the graceful chromatic number of some graphs.

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The Graceful Chromatic Number for Some Particular Classes of Graphs

Cited by 7 publications

References 3 publications

Pewarnaan Graceful Pada Graf Hasil Operasi Comb Graf Siklus Dan Graf Star

Pewarnaan Graceful Pada Graf Hasil Operasi Comb Graf Siklus Dan Graf Star

Bilangan Kromatik Graceful pada Keluarga Graf Unicyclic

On graceful chromatic number of some graphs

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