Super \(H\)-antimagic total covering for generalized antiprism and toroidal octagonal map (Q2666458)

Summary: Let \(G\) be a graph and \(H\subseteq G\) be subgraph of \(G\). The graph \(G\) is said to be \((a, d)\)-\(H\) antimagic total graph if there exists a bijective function \(f:V(H)\cup E(H)\longrightarrow \{1, 2, 3, \dots, |V(H)| + |E(H)|\}\) such that, for all subgraphs isomorphic to \(H\), the total \(H\) weights \(W(H)=W(H)=\sum_{x \in V(H)} f(x)+\sum_{y \in E(H)} f(y)\) forms an arithmetic sequence \(a, a+d, a+2d, \dots, a+(n-1)d\), where \(a\) and \(d\) are positive integers and \(n\) is the number of subgraphs isomorphic to \(H\). An \((a, d)\)-\(H\) antimagic total labeling \(f\) is said to be super if the vertex labels are from the set \(\{1, 2, \dots, |V(G)\}\). In this paper, we discuss super \((a, d)\)-\(C_3\)-antimagic total labeling for generalized antiprism and a super \((a, d)\)-\(C_8\)-antimagic total labeling for toroidal octagonal map.