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All Journal Jurnal Pengabdian Pada Masyarakat Limits: Journal of Mathematics and Its Applications Prosiding Seminar Nasional Program Pengabdian Masyarakat Jurnal Pengabdian Mandiri Jurnal Pelita: Jurnal Pembelajaran IPA Terpadu
Aditya Putra Pratama
Institut Teknologi Kalimantan
Agriculture, Biological Sciences & Forestry Humanities Chemical Engineering, Chemistry & Bioengineering Chemistry Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Engineering Languange, Linguistic, Communication & Media Mathematics Medicine & Pharmacology Physics Social Sciences Other

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Journal : Limits: Journal of Mathematics and Its Applications

 1 
Dekomposisi H-Super Anti Ajaib Atas Graf C_n ⊳_o S_n Aditya Putra Pratama; Winarni Winarni; Tiara Uni Raudyna
Limits: Journal of Mathematics and Its Applications Vol 21, No 1 (2024)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v21i1.19581

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.
Co-Authors Abrari Noor Hasmi Ariyadi Ariyadi Gusti Ahmad Fanshuri Hairudin Hairudin Lovinta Happy Atrinawati M Ihsan Alfani Putera, M Ihsan Alfani Merizka Listyaningrum Muliady Faisal Natasia, Sri Rahayu Prabowo, I Putu Deny Arthawan Sugih Ramadhan Paninggalih Rani Meliyana Roby Kurniawan Satria Shano Soleh Ardiansyah Suci Noorjannah Syalam Ali Wira Dinata Simatupang Tazkya Humaira Tegar Palyus Fiqar Tiara Uni Raudyna Vinda Daningrum Winarni Winarni Yuyun Tri Wiranti