On Rainbow Vertex Antimagic Coloring of Graphs: A New Notion

Marsidi, Marsidi; Agustin, Ika Hesti; Dafik, Dafik; Kurniawati, Elsa Yuli

doi:10.18860/ca.v7i1.12796

Cited by 4 publications

(3 citation statements)

References 10 publications

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“…In determining the exact value of rainbow vertex antimagic connection number of graph 𝐺 (𝑟𝑣𝑎𝑐(𝐺)), a lower bound is needed. The lower bound of 𝑟𝑣𝑎𝑐(𝐺) has been found by Marsidi, et al For more details see [12]. The lower bound of 𝑟𝑣𝑎𝑐(𝐺) that found by Marsidi, et al is as follows.…”

Section: Preliminariesmentioning

confidence: 54%

“…Septory et al [11] developed rainbow coloring into rainbow antimagic coloring, while Marsidi et al developed rainbow vertex coloring into rainbow vertex antimagic coloring. A formal definition related to rainbow vertex antimagic coloring can be seen in [12]. In this paper, we determine the upper bound of the rainbow vertex antimagic connection number of cycle graph (𝑟𝑣𝑎𝑐(𝐶 𝑛 )).…”

Section: Introductionmentioning

confidence: 99%

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Developing A Secure Cryptosystem with Rainbow Vertex Antimagic Coloring of Cycle Graph

Marsidi

2022

J. Mat. Mantik

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An edge labeling of graph G is a function g from the edge set of graph G to the first natural numbers up to the number of the edge set. Graph G admits a rainbow vertex antimagic coloring if, for any two vertices, there is a path with different colors of all internal vertices. The vertex color of graph G is assigned by vertex weight. The vertex weight of graph G is obtained by summing all edge labels that incident with that vertex. The rainbow vertex antimagic connection number of graph G, denoted by rvac(G) is the smallest number of different colors induced by rainbow vertex antimagic coloring. In this research, we determine the upper bound of the rainbow vertex antimagic connection number (rvac) on a cycle graph (Cn) and create a secured cryptosystem using a modified Affine Cipher based on rainbow vertex antimagic coloring.

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Section: Preliminariesmentioning

confidence: 54%

Section: Introductionmentioning

confidence: 99%

Developing A Secure Cryptosystem with Rainbow Vertex Antimagic Coloring of Cycle Graph

Marsidi

2022

J. Mat. Mantik

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“…One of the topics owned by graph theory is rainbow vertex antimagic coloring. Where rainbow vertex antimagic coloring (RVAC) is a combination of rainbow vertex coloring and vertex antimagic labeling (Marsidi et al, 2021). The use of RVAC in everyday life problems can be exemplified in the decision to color batik motif designs.…”

Section: Introductionmentioning

confidence: 99%

The Development of RBL-STEAM Learning Materials to Improve Student’s Metaliteracy Thinking Skills in Solving RVAC Problems and It’s Application on Design Motif Batik

Kamila,

Dafik,

Tirta

2023

ijcsrr

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Education is a milestone in the development of every individual’s mindset. With the development of the times, it is necessary to adjust in the field of education. One way is by developing learning tools using the research-based learning-STEAM model which aims to improve students’ meta literacy thinking skills. The method to be used in this research is a mixed method and the research procedure to be used, namely in the form of 4D development research consists of the defining stage, the design stage, the development stage, and the dissemination stage. From the device development process, the validation score obtained in each device is 3.6 for RTM, 3.5 for LKM, 3.5 for meta literacy skills test, 3.5 for the response questionnaire, 3.5 for implementation observation, 3.4 for activity observation, and 3.56 for the questionnaire. The practicality test of the learning device obtained 3.89 with a percentage of 97.25%. The effectiveness test was divided into the completeness of the meta-literation skills test with 85% of students completed, analysis of student activities with 95.5% activity, and 81.8% for the results of positive student questionnaire responses. The device as a whole meets the criteria of validity, practicality, and effectiveness. Furthermore, the Chi-Square test was conducted. Chi-Square test results obtained Asymp. Sig. 0.004 <0.05, which means that there is an increase in the distribution of student meta-literacy skill test levels from those that tend to gather in low-medium thinking abilities with 17 low-level students and 10 medium-level students at the pre-test, to those that tend to gather in the medium-high meta literacy thinking category with 11 medium-level students and 12 high-level students at the post-test.

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The rainbow vertex antimagic coloring of tree graphs

Marsidi¹,

Agustin

Dafik

et al. 2022

J. Phys.: Conf. Ser.

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Let G(V (G),E(G)) be a connected, simple, and finite graph. Let f be a bijective function of labeling on graph G from the edge set E(G) to natural number up to the number of edges of G. A rainbow vertex antimagic labeling of graph G is a function f under the condition all internal vertices of a path u – υ, Ɐu, υ ∈ V (G) have different weight (denoted by w(u)), where w(u) = ∑ uu′∈E(G)f (uu′). If G has a rainbow vertex antimagic labeling, then G is a rainbow vertex antimagic coloring, where the every vertex is assigned with the color w(u). The rvac(G) is a notation of rainbow vertex antimagic connection number of graph G which means the minimum colors taken over all rainbow vertex antimagic coloring induced by rainbow vertex antimagic labeling of graph G. The results of this research are the exact value of the rainbow vertex antimagic connection number of star (Sn ), double star (DSn ), and broom graph (Brn, m ).

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On Rainbow Vertex Antimagic Coloring of Graphs: A New Notion

Cited by 4 publications

References 10 publications

Developing A Secure Cryptosystem with Rainbow Vertex Antimagic Coloring of Cycle Graph

Developing A Secure Cryptosystem with Rainbow Vertex Antimagic Coloring of Cycle Graph

The Development of RBL-STEAM Learning Materials to Improve Student’s Metaliteracy Thinking Skills in Solving RVAC Problems and It’s Application on Design Motif Batik

The rainbow vertex antimagic coloring of tree graphs

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