Stacked book graphs are cycle-antimagic

• Main Authors: Xinqiang Ma, Muhammad Awais Umar, Saima Nazeer, Yu-Ming Chu, Youyuan Liu
• Format: Article
• Language: English
• Published: AIMS Press 2020-07-01
• Series: AIMS Mathematics
• Subjects: 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
• Online Access: https://www.aimspress.com/article/10.3934/math.2020387/fulltext.html

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.