On rainbow antimagic coloring of graphs

Budi, Hermawan Setyo; Dafik, Dafik; Tirta, I Made; Agustin, Ika Hesti; Kristiana, Arika Indah

doi:10.1088/1742-6596/1832/1/012016

Cited by 14 publications

(12 citation statements)

References 6 publications

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“…First, we prove the correctness of the lower bound of rac(H 4 ) is rac(H 4 ) ≥ mn + 2. We know that H 4 graph is P (3,n) graph which is copied as many as m. Based on Theorem 3 [4], so that H 4 graph requires as many colors as mn + 2. So we got that the lower bound of rac(H 4 ) is rac(H 4 ) ≥ mn + 2 with m, n ≥ 2.…”

Section: Resultsmentioning

confidence: 99%

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On the rainbow antimagic coloring of vertex amalgamation of graphs

Joedo

Dafik

Kristiana

et al. 2022

J. Phys.: Conf. Ser.

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The purpose of this study is to develop rainbow antimagic coloring. This study is a combination of two notions, namely antimagic and rainbow concept. If every vertex of graph G is labeled with the antimagic labels and then edge weight of antimagic labels are used to assign a rainbow coloring. The minimum number of colors for a rainbow path to exist with the condition satisfying the edge weights w(x) ≠ w(y) for any two vertices x and y is the definition of the rainbow antimagic connection number rac(G). In this study, we use connected graphs and simple graphs in obtaining the rainbow antimagic connection number. This paper will explain the rainbow antimagic coloring on some graphs and get their formula of the rainbow antimagic connection number. We have obtained rac(G) where G is vertex amalgamation of graphs, namely path, star, broom, paw, fan, and triangular book graph.

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Section: Resultsmentioning

confidence: 99%

“…Sulistiono et al [24] made a theorem to prove the lower bound of rac(G). More study on rainbow antimagic coloring can be seen at [1,4,9,22].…”

Section: Introductionmentioning

confidence: 99%

On the rainbow antimagic coloring of vertex amalgamation of graphs

Joedo

Dafik

Kristiana

et al. 2022

J. Phys.: Conf. Ser.

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“…Definition 3 . [5] Misalkan G adalah suatu graf simpel dan terkoneksi. Sebuah fungsi bijektif f : V (G) → {1, 2, ..., V (G)}, memiliki bobot setiap sisi uv ∈ E(G) dalam F adalah w f (uv) = f (u) + f (v).…”

Section: Pendahuluanunclassified

Analisis Rainbow Antimagic Coloring Pada Hasil Operasi Comb Graf Lintasan

Suryandana

2022

CGANT. JOU. OF MATH. AND APP.

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All the graphs in this paper are connected graphs. Let $G=(V,E)$ where $V(G)$ is a set of vertex from graph $G$ while $E(G)$ is a set of edge from graph $G$. A bijection function $f: V \rightarrow \{1,2,3,...,\lvert V(G)\rvert\}$ the associated weight of an edge $uv \in E(G)$ under $f$ is $W_f{(uv)}=f(u)+f(v)$. A path $P$ in a vertex-labeled graph $G$ is said to be a rainbow path if for every two edges $uv$, $u'v' \in E(P)$, there is $w_f{(uv)}\neq w_f{u'v'}$. If for every two vertices $u$ and $v$ of $G$, there is a rainbow $u$-$v$ path, then $f$ is called a rainbow antimagic labeling of $G$. A graph $G$ is rainbow antimagic if $G$ has a rainbow antimagic labeling. The minimum number of color needed to make $G$ rainbow connected, called rainbow antimagic connection number, denoted by rac(G). In this paper, we will analyze the rainbow antimagic coloring on comb product of path graph.

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“…In this study, we initiate to combine the two notion, namely rainbow coloring and antimagic labeling [14] [15]. We name for this combination as rainbow vertex antimagic coloring.…”

Section: 𝑢𝑣∈𝐸(𝐺)mentioning

confidence: 99%

On Rainbow Vertex Antimagic Coloring of Graphs: A New Notion

Marsidi

Agustin

Dafik

et al. 2021

CAUCHY

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All graph in this paper are simple, finite, and connected. Let be a labeling of a graph . The function is called antimagic rainbow edge labeling if for any two vertices and , all internal vertices in path have different weight, where the weight of vertex is the sum of its incident edges label. The vertex weight denoted by for every . If G has a antimagic rainbow edge labeling, then is a antimagic rainbow vertex connection, where the every vertex is assigned with the color . The antimagic rainbow vertex connection number of , denoted by , is the minimum colors taken over all rainbow vertex connection induced by antimagic rainbow edge labeling of . In this paper, we determined the exact value of the antimagic rainbow vertex connection number of path ( ), wheel ( ), friendship ( ), and fan ( ).

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On rainbow antimagic coloring of graphs

Cited by 14 publications

References 6 publications

On the rainbow antimagic coloring of vertex amalgamation of graphs

On the rainbow antimagic coloring of vertex amalgamation of graphs

Analisis Rainbow Antimagic Coloring Pada Hasil Operasi Comb Graf Lintasan

On Rainbow Vertex Antimagic Coloring of Graphs: A New Notion

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