Reflexive edge strength of convex polytopes and corona product of cycle with path
For a graph $ G $, we define a total $ k $-labeling $ \varphi $ is a combination of an edge labeling $ \varphi_e(x)\to\{1, 2, \ldots, k_e\} $ and a vertex labeling $ \varphi_v(x) \to \{0, 2, \ldots, 2k_v\} $, such that $ \varphi(x) = \varphi_v(x) $ if $ x\in V(G) $ and $ \varphi(x) = \varphi_e(x) $...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-04-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022657?viewType=HTML |
| _version_ | 1818270416473423872 |
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| author | Kooi-Kuan Yoong Roslan Hasni Gee-Choon Lau Muhammad Ahsan Asim Ali Ahmad |
| author_facet | Kooi-Kuan Yoong Roslan Hasni Gee-Choon Lau Muhammad Ahsan Asim Ali Ahmad |
| author_sort | Kooi-Kuan Yoong |
| collection | DOAJ |
| description | For a graph $ G $, we define a total $ k $-labeling $ \varphi $ is a combination of an edge labeling $ \varphi_e(x)\to\{1, 2, \ldots, k_e\} $ and a vertex labeling $ \varphi_v(x) \to \{0, 2, \ldots, 2k_v\} $, such that $ \varphi(x) = \varphi_v(x) $ if $ x\in V(G) $ and $ \varphi(x) = \varphi_e(x) $ if $ x\in E(G) $, then $ k = \, \mbox{max}\, \{k_e, 2k_v\} $. The total $ k $-labeling $ \varphi $ is an <i>edge irregular reflexive $ k $-labeling</i> of $ G $ if every two different edges $ xy $ and $ x^\prime y^\prime $, the edge weights are distinct. The smallest value $ k $ for which such labeling exists is called a <i>reflexive edge strength</i> of $ G $. In this paper, we focus on the edge irregular reflexive labeling of antiprism, convex polytopes $ \mathcal D_{n} $, $ \mathcal R_{n} $, and corona product of cycle with path. This study also leads to interesting open problems for further extension of the work. |
| first_indexed | 2024-12-12T21:09:56Z |
| format | Article |
| id | doaj.art-a0df1e3a4592412b9255d87f840d858b |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-12T21:09:56Z |
| publishDate | 2022-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-a0df1e3a4592412b9255d87f840d858b2022-12-22T00:11:55ZengAIMS PressAIMS Mathematics2473-69882022-04-0177117841180010.3934/math.2022657Reflexive edge strength of convex polytopes and corona product of cycle with pathKooi-Kuan Yoong0Roslan Hasni1Gee-Choon Lau2Muhammad Ahsan Asim 3Ali Ahmad41. Special Interest Group on Modelling and Data Analytics (SIGMDA), Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Terengganu, Malaysia1. Special Interest Group on Modelling and Data Analytics (SIGMDA), Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Terengganu, Malaysia2. Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (Segamat Campus), Johor, Malaysia3. College of Computer Sciences and Information Technology, Jazan University, Jazan, Saudi Arabia3. College of Computer Sciences and Information Technology, Jazan University, Jazan, Saudi ArabiaFor a graph $ G $, we define a total $ k $-labeling $ \varphi $ is a combination of an edge labeling $ \varphi_e(x)\to\{1, 2, \ldots, k_e\} $ and a vertex labeling $ \varphi_v(x) \to \{0, 2, \ldots, 2k_v\} $, such that $ \varphi(x) = \varphi_v(x) $ if $ x\in V(G) $ and $ \varphi(x) = \varphi_e(x) $ if $ x\in E(G) $, then $ k = \, \mbox{max}\, \{k_e, 2k_v\} $. The total $ k $-labeling $ \varphi $ is an <i>edge irregular reflexive $ k $-labeling</i> of $ G $ if every two different edges $ xy $ and $ x^\prime y^\prime $, the edge weights are distinct. The smallest value $ k $ for which such labeling exists is called a <i>reflexive edge strength</i> of $ G $. In this paper, we focus on the edge irregular reflexive labeling of antiprism, convex polytopes $ \mathcal D_{n} $, $ \mathcal R_{n} $, and corona product of cycle with path. This study also leads to interesting open problems for further extension of the work. https://www.aimspress.com/article/doi/10.3934/math.2022657?viewType=HTMLconvex polytopecorona productedge irregular reflexive labelingplane graphreflexive edge strength |
| spellingShingle | Kooi-Kuan Yoong Roslan Hasni Gee-Choon Lau Muhammad Ahsan Asim Ali Ahmad Reflexive edge strength of convex polytopes and corona product of cycle with path AIMS Mathematics convex polytope corona product edge irregular reflexive labeling plane graph reflexive edge strength |
| title | Reflexive edge strength of convex polytopes and corona product of cycle with path |
| title_full | Reflexive edge strength of convex polytopes and corona product of cycle with path |
| title_fullStr | Reflexive edge strength of convex polytopes and corona product of cycle with path |
| title_full_unstemmed | Reflexive edge strength of convex polytopes and corona product of cycle with path |
| title_short | Reflexive edge strength of convex polytopes and corona product of cycle with path |
| title_sort | reflexive edge strength of convex polytopes and corona product of cycle with path |
| topic | convex polytope corona product edge irregular reflexive labeling plane graph reflexive edge strength |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022657?viewType=HTML |
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