Stacked book graphs are cycle-antimagic
A family of subgraphs of a finite, simple and connected graph $G$ is called an <em>edge covering</em> of $G$ if every edge of graph $G$ belongs to at least one of the subgraphs. In this manuscript, we define the edge covering of a stacked book graph and its uniform subdivision by cycles...
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AIMS Press
2020-07-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2020387/fulltext.html |
| _version_ | 1818284781580845056 |
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| author | Xinqiang Ma Muhammad Awais Umar Saima Nazeer Yu-Ming Chu Youyuan Liu |
| author_facet | Xinqiang Ma Muhammad Awais Umar Saima Nazeer Yu-Ming Chu Youyuan Liu |
| author_sort | Xinqiang Ma |
| collection | DOAJ |
| description | A family of subgraphs of a finite, simple and connected graph $G$ is called an <em>edge covering</em> of $G$ if every edge of graph $G$ belongs to at least one of the subgraphs. In this manuscript, we define the edge covering of a stacked book graph and its uniform subdivision by cycles of different lengths. If every subgraph of $G$ is isomorphic to one graph $H$ (say) and there is a bijection $\phi:V(G)\cup E(G) \to \{1,2,\dots, |V(G)|+|E(G)| \}$ such that $wt_{\phi}(H)$ forms an arithmetic progression then such a graph is called $(\alpha,d)$-$H$-antimagic.<br />
In this paper, we prove super $(\alpha,d)$-cycle-antimagic labelings of stacked book graphs and $r$ subdivided stacked book graph. |
| first_indexed | 2024-12-13T00:58:16Z |
| format | Article |
| id | doaj.art-9867424aa83f4b349e4f8a0026fc8daf |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-13T00:58:16Z |
| publishDate | 2020-07-01 |
| publisher | AIMS Press |
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| series | AIMS Mathematics |
| spelling | doaj.art-9867424aa83f4b349e4f8a0026fc8daf2022-12-22T00:04:44ZengAIMS PressAIMS Mathematics2473-69882020-07-01566043605010.3934/math.2020387Stacked book graphs are cycle-antimagicXinqiang Ma0Muhammad Awais Umar1Saima Nazeer2Yu-Ming Chu3Youyuan Liu41 College of Computer Science and Technology, Guizhou University, Guiyang, China 2 Institute of Intelligent Computing and Visualization based on Big Data,Chongqing University of Arts and Sciences, Chongqing, China3 Govt. Degree College (B), Sharaqpur Sharif, 39460, Pakistan4 Department of Mathematics, Lahore College for Women University, Lahore, 54660, Pakistan5 Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China 6 Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, P. R. China2 Institute of Intelligent Computing and Visualization based on Big Data,Chongqing University of Arts and Sciences, Chongqing, ChinaA family of subgraphs of a finite, simple and connected graph $G$ is called an <em>edge covering</em> of $G$ if every edge of graph $G$ belongs to at least one of the subgraphs. In this manuscript, we define the edge covering of a stacked book graph and its uniform subdivision by cycles of different lengths. If every subgraph of $G$ is isomorphic to one graph $H$ (say) and there is a bijection $\phi:V(G)\cup E(G) \to \{1,2,\dots, |V(G)|+|E(G)| \}$ such that $wt_{\phi}(H)$ forms an arithmetic progression then such a graph is called $(\alpha,d)$-$H$-antimagic.<br /> In this paper, we prove super $(\alpha,d)$-cycle-antimagic labelings of stacked book graphs and $r$ subdivided stacked book graph.https://www.aimspress.com/article/10.3934/math.2020387/fulltext.htmlbook graphstacked book graph $sb_{(pq)}$$r$ subdivided stacked book graph $sb_{(pq)}(r)$super $(\alphad)$-$c_4$-antimagic labelingd)$-$c_{4(r+1)}$-antimagic labeling |
| spellingShingle | Xinqiang Ma Muhammad Awais Umar Saima Nazeer Yu-Ming Chu Youyuan Liu Stacked book graphs are cycle-antimagic AIMS Mathematics book graph stacked book graph $sb_{(p q)}$ $r$ subdivided stacked book graph $sb_{(p q)}(r)$ super $(\alpha d)$-$c_4$-antimagic labeling d)$-$c_{4(r+1)}$-antimagic labeling |
| title | Stacked book graphs are cycle-antimagic |
| title_full | Stacked book graphs are cycle-antimagic |
| title_fullStr | Stacked book graphs are cycle-antimagic |
| title_full_unstemmed | Stacked book graphs are cycle-antimagic |
| title_short | Stacked book graphs are cycle-antimagic |
| title_sort | stacked book graphs are cycle antimagic |
| topic | book graph stacked book graph $sb_{(p q)}$ $r$ subdivided stacked book graph $sb_{(p q)}(r)$ super $(\alpha d)$-$c_4$-antimagic labeling d)$-$c_{4(r+1)}$-antimagic labeling |
| url | https://www.aimspress.com/article/10.3934/math.2020387/fulltext.html |
| work_keys_str_mv | AT xinqiangma stackedbookgraphsarecycleantimagic AT muhammadawaisumar stackedbookgraphsarecycleantimagic AT saimanazeer stackedbookgraphsarecycleantimagic AT yumingchu stackedbookgraphsarecycleantimagic AT youyuanliu stackedbookgraphsarecycleantimagic |