Total Distance Vertex Irregularity Strength of Hairy Cycle C_m^n Graph
A total graph labeling is an assignment of integers to the union of vertices and edges to certain conditions. The labeling becomes D -distance vertex irregular total k-labeling when each vertex of G has a different weight (which is determined by D-distance neighborhood). The total distance vertex ir...
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INTI International University
2022
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| Online Access: | http://eprints.intimal.edu.my/1662/ http://eprints.intimal.edu.my/1662/1/jods2022_09.pdf |
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| author | Ida, Wijayanti Dian Eka, Wijayanti Sugiyarto, Surono |
| author_facet | Ida, Wijayanti Dian Eka, Wijayanti Sugiyarto, Surono |
| author_sort | Ida, Wijayanti |
| building | INTI Institutional Repository |
| collection | Online Access |
| description | A total graph labeling is an assignment of integers to the union of vertices and edges to certain conditions. The labeling becomes D -distance vertex irregular total k-labeling when each vertex of G has a different weight (which is determined by D-distance neighborhood). The total distance vertex irregularity strength of G denoted by tdis(G) and define as the minimum of the biggest label k over all D-distance vertex irregular total k-labelings of G. In this paper, we investigate about D-distance vertex irregular total k-labelings on hairy cycle C_m^n graphs which can be applied to cryptography and computational networks. The unique hairy cycle graph construction makes the weights of each vertex of this graph different and random. Therefore, this weight formula can be applied in stream cipher cryptography as a key generator. To obtained the formula labeling, we carried out labeling experiments repeatedly to find labeling patterns and then formulate it into a labeling function. We also provide the lower bound and determine the value of total distance vertex irregularity strength of hairy cycle C_m^n graphs. we prove that for m=2,3,4, n≥5 an odd positive integer , hairy cycle C_m^n graphs admits an D-distance vertex irregular total k-labelings with total distance vertex irregularity strength, tdis(C_m^n )=⌈(mn+1)/2⌉. |
| first_indexed | 2025-11-14T11:56:53Z |
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| institution | INTI International University |
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| language | English |
| last_indexed | 2025-11-14T11:56:53Z |
| publishDate | 2022 |
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| spelling | intimal-16622024-05-07T09:43:24Z http://eprints.intimal.edu.my/1662/ Total Distance Vertex Irregularity Strength of Hairy Cycle C_m^n Graph Ida, Wijayanti Dian Eka, Wijayanti Sugiyarto, Surono Q Science (General) QA Mathematics QA75 Electronic computers. Computer science A total graph labeling is an assignment of integers to the union of vertices and edges to certain conditions. The labeling becomes D -distance vertex irregular total k-labeling when each vertex of G has a different weight (which is determined by D-distance neighborhood). The total distance vertex irregularity strength of G denoted by tdis(G) and define as the minimum of the biggest label k over all D-distance vertex irregular total k-labelings of G. In this paper, we investigate about D-distance vertex irregular total k-labelings on hairy cycle C_m^n graphs which can be applied to cryptography and computational networks. The unique hairy cycle graph construction makes the weights of each vertex of this graph different and random. Therefore, this weight formula can be applied in stream cipher cryptography as a key generator. To obtained the formula labeling, we carried out labeling experiments repeatedly to find labeling patterns and then formulate it into a labeling function. We also provide the lower bound and determine the value of total distance vertex irregularity strength of hairy cycle C_m^n graphs. we prove that for m=2,3,4, n≥5 an odd positive integer , hairy cycle C_m^n graphs admits an D-distance vertex irregular total k-labelings with total distance vertex irregularity strength, tdis(C_m^n )=⌈(mn+1)/2⌉. INTI International University 2022-08 Article PeerReviewed text en cc_by_4 http://eprints.intimal.edu.my/1662/1/jods2022_09.pdf Ida, Wijayanti and Dian Eka, Wijayanti and Sugiyarto, Surono (2022) Total Distance Vertex Irregularity Strength of Hairy Cycle C_m^n Graph. Journal of Data Science, 2022 (09). pp. 1-12. ISSN 2805-5160 http://ipublishing.intimal.edu.my/jods.html |
| spellingShingle | Q Science (General) QA Mathematics QA75 Electronic computers. Computer science Ida, Wijayanti Dian Eka, Wijayanti Sugiyarto, Surono Total Distance Vertex Irregularity Strength of Hairy Cycle C_m^n Graph |
| title | Total Distance Vertex Irregularity Strength of Hairy Cycle C_m^n Graph |
| title_full | Total Distance Vertex Irregularity Strength of Hairy Cycle C_m^n Graph |
| title_fullStr | Total Distance Vertex Irregularity Strength of Hairy Cycle C_m^n Graph |
| title_full_unstemmed | Total Distance Vertex Irregularity Strength of Hairy Cycle C_m^n Graph |
| title_short | Total Distance Vertex Irregularity Strength of Hairy Cycle C_m^n Graph |
| title_sort | total distance vertex irregularity strength of hairy cycle c_m^n graph |
| topic | Q Science (General) QA Mathematics QA75 Electronic computers. Computer science |
| url | http://eprints.intimal.edu.my/1662/ http://eprints.intimal.edu.my/1662/ http://eprints.intimal.edu.my/1662/1/jods2022_09.pdf |