Stacked book graphs are cycle-antimagic

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.

Keywords

• 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