Stacked book graphs are cycle-antimagic

Xinqiang Ma; Muhammad Awais Umar; Saima Nazeer; Yu-Ming Chu; Youyuan Liu; Xinqiang Ma; Muhammad Awais Umar; Saima Nazeer; Yu-Ming Chu; Youyuan Liu

doi:10.3934/math.2020387

AIMS Mathematics

2020, Volume 5, Issue 6: 6043-6050. doi: 10.3934/math.2020387

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Research article

Stacked book graphs are cycle-antimagic

1.
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, China
3.
Govt. Degree College (B), Sharaqpur Sharif, 39460, Pakistan
4.
Department of Mathematics, Lahore College for Women University, Lahore, 54660, Pakistan
5.
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. China

Received: 26 April 2020 Accepted: 15 July 2020 Published: 23 July 2020
MSC : 05C78, 05C70

A family of subgraphs of a finite, simple and connected graph $G$ is called an edge covering 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. In this paper, we prove super $(\alpha, d)$-cycle-antimagic labelings of stacked book graphs and $r$ subdivided stacked book graph.
Citation: Xinqiang Ma, Muhammad Awais Umar, Saima Nazeer, Yu-Ming Chu, Youyuan Liu. Stacked book graphs are cycle-antimagic[J]. AIMS Mathematics, 2020, 5(6): 6043-6050. doi: 10.3934/math.2020387

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Abstract

A family of subgraphs of a finite, simple and connected graph $G$ is called an edge covering 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. In this paper, we prove super $(\alpha, d)$-cycle-antimagic labelings of stacked book graphs and $r$ subdivided stacked book graph.

References

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