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.

中文翻译：

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堆积的书​​形图具有周期反作用力

如果图$ G $的每个边都属于至少一个子图，则有限，简单和连通图$ G $的子图族称为$ G $的边覆盖。在此手稿中，我们通过不同长度的循环来定义堆积书形图的边缘覆盖及其均匀细分。如果$ G $的每个子图与一个图$ H $同构（例如），并且有一个双射$ \ phi：V（G）\ cup E（G）\ to \ {1,2，\ dots，| V （G）| + | E（G）| \} $，使得$ wt _ {\ phi}（H）$形成算术级数，则这种图形称为$（\ alpha，d）$-$ H $-反魔术。
在本文中，我们证明了堆叠的书形图和$ r $细分的堆叠的书形图的超级$（\ alpha，d）$-周期-反魔术标签。