SuperH-Antimagic Total Covering for Generalized Antiprism and Toroidal Octagonal Map (original) (raw)

2021, Journal of Mathematics

LetGbe a graph andH⊆Gbe subgraph ofG. The graphGis said to bea,d-Hantimagic total graph if there exists a bijective functionf:VH∪EH⟶1,2,3,…,VH+EHsuch that, for all subgraphs isomorphic toH, the totalHweightsWH=WH=∑x∈VHfx+∑y∈EHfyforms an arithmetic sequencea,a+d,a+2d,…,a+n−1d, whereaanddare positive integers andnis the number of subgraphs isomorphic toH. Ana,d-Hantimagic total labelingfis said to be super if the vertex labels are from the set1,2,…,|VG. In this paper, we discuss supera,d-C3-antimagic total labeling for generalized antiprism and a supera,d-C8-antimagic total labeling for toroidal octagonal map.