### Dekomposisi H-Super Anti Ajaib Atas Graf C_n ⊳_o S_n

Aditya Putra Pratama, Winarni Winarni, Tiara Uni Raudyna

#### Abstract

The concept of an H-Magic decomposition of a graph G is formed based on the concept of decomposition and the concept of labeling a graph. The set A={H_1,H_2,…,H_k } subgraphs of graph G is a decomposition of G if ⋃_(1≤i≤k)▒H_i =G and E(H_i )∩E(H_j )=∅  for i≠j. If every subgraph H_i which is the result of the decomposition of graph G is isomorphic to a subgraph H of G, then ={H_1,H_2,…,H_k } is an H-decomposition of G. Graph G is said to be H-Magic decomposition, if there is a bijective mapping :V(G)∪E(G)→{1,2,…,|V(G)|+|E(G)|} such that the total weight of the vertices and edges for each subgraph H_i is constant. If the total labels of vertices and edges for each subgraph H_i form an arithmetic progression with a difference of each weight of subgraph is one, then graph G is said to be H-Anti Magic decomposition. In this study, the H-Super Anti Magic decomposition of the graph C_n  ⊳_o  S_n is investigated. First, we investigate the characteristics of the graph C_n ⊳_o S_n along with the selected subgraphs. Next, based on the selected subgraph, a labeling pattern is formed on the graph C_n ⊳_o S_n such that the total weight of each subgraph forms an arithmetic sequence with the difference is one. From the labeling pattern, a bijective labeling function is formed using an arithmetic sequence approach. Based on the labeling function, it is shown that the subgraphs of C_n ⊳_o S_n are an H-decomposition of C_n ⊳_o S_n. The final result of this research is the graph C_n  ⊳_o  S_n contains the H-Super Anti Magic decomposition with magic constant 〖w_n (H〗_i)=〖2n〗^3+〖4n〗^2+3n+2+i for 1 ≤i<n, and 〖w_n (H〗_i)=〖2n〗^3+〖4n〗^2+3n+2  for i=n, where n≥3, n∈N.

#### Keywords

decomposition; graph; H-(super)Anti Magic; labelling; subgraph

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#### References

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DOI: http://dx.doi.org/10.12962/limits.v21i1.19581

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