On rainbow vertex antimagic coloring and its application to the encryption keystream construction
Let G = (V,E) be a graph that is a simple, connected and un-directed graph. We now introduce a new notion of rainbow vertex antimagic coloring. This is a proper development of antimagic labeling with rainbow vertex coloring. The weight of a vertex v ∈ V(G) under f for f : E(G) → {1,2, …, |E(G)|} is...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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Natural Sciences Publishing
2024
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| Online Access: | http://psasir.upm.edu.my/id/eprint/112470/ http://psasir.upm.edu.my/id/eprint/112470/1/js5241km6556q7.pdf |
| _version_ | 1848865951070552064 |
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| author | Agustin, Ika Hesti Dafik, Dafik Nisviasari, Rosanita Baihaki, Rifki Ilham Kurniawati, Elsa Yuli Husain, Sharifah Kartini Said Nagaraja, Vaishnavi |
| author_facet | Agustin, Ika Hesti Dafik, Dafik Nisviasari, Rosanita Baihaki, Rifki Ilham Kurniawati, Elsa Yuli Husain, Sharifah Kartini Said Nagaraja, Vaishnavi |
| author_sort | Agustin, Ika Hesti |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Let G = (V,E) be a graph that is a simple, connected and un-directed graph. We now introduce a new notion of rainbow vertex antimagic coloring. This is a proper development of antimagic labeling with rainbow vertex coloring. The weight of a vertex v ∈ V(G) under f for f : E(G) → {1,2, …, |E(G)|} is wf (v) = S e∈E(v) f (e), where E(v) is the set of vertices incident to v. If each vertex has a different weight, afterwards the function f is also referred to as vertex antimagic edge labeling. If all internal vertices on the u−v path have different edge weights for each vertex u and v, afterwards the path is assumed to be a rainbow path. The minimum amount of colors assigned over all rainbow colorings that result from rainbow vertex antimagic labelings of G is the rainbow vertex antimagic connection number of G, rvac(G). For the purpose of trying to find some new lemmas or theorems about rvac(G), we will prove the specific value of the rainbow vertex antimagic connection number of a specific family of graphs in this paper. Furthermore, based on our obtained lemmas and theorems, we use it for constructing an encryption keystream for robust symmetric cryptography. Moreover, to test the robustness of our model, we compare it with normal symmetric cryptography such as AES and DES. |
| first_indexed | 2025-11-15T14:12:51Z |
| format | Article |
| id | upm-112470 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T14:12:51Z |
| publishDate | 2024 |
| publisher | Natural Sciences Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1124702024-09-25T08:24:51Z http://psasir.upm.edu.my/id/eprint/112470/ On rainbow vertex antimagic coloring and its application to the encryption keystream construction Agustin, Ika Hesti Dafik, Dafik Nisviasari, Rosanita Baihaki, Rifki Ilham Kurniawati, Elsa Yuli Husain, Sharifah Kartini Said Nagaraja, Vaishnavi Let G = (V,E) be a graph that is a simple, connected and un-directed graph. We now introduce a new notion of rainbow vertex antimagic coloring. This is a proper development of antimagic labeling with rainbow vertex coloring. The weight of a vertex v ∈ V(G) under f for f : E(G) → {1,2, …, |E(G)|} is wf (v) = S e∈E(v) f (e), where E(v) is the set of vertices incident to v. If each vertex has a different weight, afterwards the function f is also referred to as vertex antimagic edge labeling. If all internal vertices on the u−v path have different edge weights for each vertex u and v, afterwards the path is assumed to be a rainbow path. The minimum amount of colors assigned over all rainbow colorings that result from rainbow vertex antimagic labelings of G is the rainbow vertex antimagic connection number of G, rvac(G). For the purpose of trying to find some new lemmas or theorems about rvac(G), we will prove the specific value of the rainbow vertex antimagic connection number of a specific family of graphs in this paper. Furthermore, based on our obtained lemmas and theorems, we use it for constructing an encryption keystream for robust symmetric cryptography. Moreover, to test the robustness of our model, we compare it with normal symmetric cryptography such as AES and DES. Natural Sciences Publishing 2024 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/112470/1/js5241km6556q7.pdf Agustin, Ika Hesti and Dafik, Dafik and Nisviasari, Rosanita and Baihaki, Rifki Ilham and Kurniawati, Elsa Yuli and Husain, Sharifah Kartini Said and Nagaraja, Vaishnavi (2024) On rainbow vertex antimagic coloring and its application to the encryption keystream construction. Applied Mathematics and Information Sciences, 18 (4). pp. 783-794. ISSN 1935-0090; EISSN: 2325-0399 https://www.naturalspublishing.com/Article.asp?ArtcID=28665 10.18576/amis/180411 |
| spellingShingle | Agustin, Ika Hesti Dafik, Dafik Nisviasari, Rosanita Baihaki, Rifki Ilham Kurniawati, Elsa Yuli Husain, Sharifah Kartini Said Nagaraja, Vaishnavi On rainbow vertex antimagic coloring and its application to the encryption keystream construction |
| title | On rainbow vertex antimagic coloring and its application to the encryption keystream construction |
| title_full | On rainbow vertex antimagic coloring and its application to the encryption keystream construction |
| title_fullStr | On rainbow vertex antimagic coloring and its application to the encryption keystream construction |
| title_full_unstemmed | On rainbow vertex antimagic coloring and its application to the encryption keystream construction |
| title_short | On rainbow vertex antimagic coloring and its application to the encryption keystream construction |
| title_sort | on rainbow vertex antimagic coloring and its application to the encryption keystream construction |
| url | http://psasir.upm.edu.my/id/eprint/112470/ http://psasir.upm.edu.my/id/eprint/112470/ http://psasir.upm.edu.my/id/eprint/112470/ http://psasir.upm.edu.my/id/eprint/112470/1/js5241km6556q7.pdf |