On the rainbow antimagic coloring of vertex amalgamation of graphs

Joedo, J C; Dafik, Dafik; Kristiana, Arika Indah; Agustin, Ika Hesti; Nisviasari, Rosanita

doi:10.1088/1742-6596/2157/1/012014

Cited by 10 publications

(5 citation statements)

References 20 publications

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“…Hasil rainbow antimagic coloring telah dipelajari pada [6], [12], [16] dan [21]. Dalam penelitian ini, kami mempelajari rainbow antimagic coloring dan menemukan nilai rainbow antimagic connection number dari graf hasil operasi join 𝐵𝑟 𝑛,3 + 𝐾 1 .…”

Section: Pendahuluanunclassified

Rainbow Antimagic Coloring pada Graf Hasil Operasi Join pada Graf Broom

Retnowardani,

Septory,

Dliou

et al. 2023

estimator

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Misalkan adalah graf terhubung dengan himpunan titik dan himpunan sisi . Fungsi bijektif dari ke himpunan adalah pelabelan titik graf . Fungsi bijektif disebut rainbow antimagic labeling jika untuk setiap dua sisi dan dalam lintasan , dengan dan . Rainbow antimagic coloring adalah pewarnaan graf dengan rainbow antimagic labeling. Jadi, setiap rainbow antimagic labeling merupakan pewarnaan pelangi graf dengan bobot sisi adalah warna sisi . Rainbow antimagic connection number pada graf adalah jumlah warna terkecil dari semua rainbow antimagic coloring graf , dinotasikan dengan . Pada penelitian ini, dipelajari rainbow antimagic coloring dan mendapatkan nilai rainbow antimagic connection number graf hasil operasi join .

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Section: Pendahuluanunclassified

Rainbow Antimagic Coloring pada Graf Hasil Operasi Join pada Graf Broom

Retnowardani,

Septory,

Dliou

et al. 2023

estimator

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“…Some other results about rainbow antimagic connection number can be found in [21][22][23][24]. In this paper, we will study the rainbow antimagic connection number of graph F n T m where F n is a friendship graph with order 2n + 1 and T m ∈ {P m , S m , Br m,p , S m,m }, where P m is the path graph of order m, S m is the star graph of order m + 1, Br m,p is the broom graph of order m + p and S m,m is the double star graph of order 2m + 2.…”

Section: Theorem 2 ([21]mentioning

confidence: 99%

On the Study of Rainbow Antimagic Connection Number of Comb Product of Friendship Graph and Tree

Septory

Susilowati²,

Dafik³

et al. 2022

Symmetry

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Given a graph G with vertex set V(G) and edge set E(G), for the bijective function f(V(G))→{1,2,⋯,|V(G)|}, the associated weight of an edge xy∈E(G) under f is w(xy)=f(x)+f(y). If all edges have pairwise distinct weights, the function f is called an edge-antimagic vertex labeling. A path P in the vertex-labeled graph G is said to be a rainbow x−y path if for every two edges xy,x′y′∈E(P) it satisfies w(xy)≠w(x′y′). The function f is called a rainbow antimagic labeling of G if there exists a rainbow x−y path for every two vertices x,y∈V(G). We say that graph G admits a rainbow antimagic coloring when we assign each edge xy with the color of the edge weight w(xy). The smallest number of colors induced from all edge weights of antimagic labeling is the rainbow antimagic connection number of G, denoted by rac(G). This paper is intended to investigate non-symmetrical phenomena in the comb product of graphs by considering antimagic labeling and optimizing rainbow connection, called rainbow antimagic coloring. In this paper, we show the exact value of the rainbow antimagic connection number of the comb product of graph Fn⊳Tm, where Fn is a friendship graph with order 2n+1 and Tm∈{Pm,Sm,Brm,p,Sm,m}, where Pm is the path graph of order m, Sm is the star graph of order m+1, Brm,p is the broom graph of order m+p and Sm,m is the double star graph of order 2m+2.

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“…Arumugam et al Rainbow antimagic coloring results have been studied in [6], [12], [16] and [21]. In this study, we studied rainbow antimagic coloring and have an exact value of rainbow antimagic connection number of join product of graph 𝐺 + 𝐾 1 where 𝐺 is graph 𝑚𝑃 𝑛 , graph 𝑚𝑆 𝑛 , graph 𝑚ℱ 𝑛 , graph 𝑚𝐹 𝑛 and graph 𝑚𝑆 𝑛,𝑛 .…”

Section: Introductionmentioning

confidence: 99%

On Rainbow Antimagic Coloring of Joint Product of Graphs

Septory

Susilowati

Dafik

et al. 2023

CAUCHY

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Let be a connected graph with vertex set and edge set . A bijection from to the set is a labeling of graph . The bijection is called rainbow antimagic vertex labeling if for any two edge and in path , where and . Rainbow antimagic coloring is a graph which has a rainbow antimagic labeling. Thus, every rainbow antimagic labeling induces a rainbow coloring G where the edge weight is the color of the edge . The rainbow antimagic connection number of graph is the smallest number of colors of all rainbow antimagic colorings of graph , denoted by . In this study, we studied rainbow antimagic coloring and have an exact value of rainbow antimagic connection number of joint product of graph where is graph , graph , graph , graph and graph .

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On the rainbow antimagic coloring of vertex amalgamation of graphs

Cited by 10 publications

References 20 publications

Rainbow Antimagic Coloring pada Graf Hasil Operasi Join pada Graf Broom

Rainbow Antimagic Coloring pada Graf Hasil Operasi Join pada Graf Broom

On the Study of Rainbow Antimagic Connection Number of Comb Product of Friendship Graph and Tree

On Rainbow Antimagic Coloring of Joint Product of Graphs

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