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All Journal KADIKMA Jurnal Daya Matematis UNEJ e-Proceeding BAREKENG: Jurnal Ilmu Matematika dan Terapan JPKMI (Jurnal Pengabdian Kepada Masyarakat Indonesia) Jurnal Ilmu Pendidikan Sekolah Dasar CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Rafiantika Megahnia Prihandini
Program Studi Pendidikan Matematika, Universitas Jember, Indonesia
Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Education Energy Engineering Environmental Science Mathematics Mechanical Engineering Physics Public Health Social Sciences Transportation Other

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Journal : UNEJ%20e-Proceeding

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Construction of Super H-Antimagicness of Graph by Uses a Partition Technique with Cancelation Number Rafiantika Megahnia Prihandini; Dafik Dafik; Ika Hesti Agustin
UNEJ e-Proceeding 2016: Proceeding The 1st International Basic Science Conference
Publisher : UPT Penerbitan Universitas Jember

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Abstract

Abstract—The graph operation is one method to construct a new graph by applying the operation to two or more graph. One of graph operation is amalgamation, let {Hi} be a finite collection of nontrivial, simple and undirected graphs and let each Hi has a fixed vertex vj called a terminal. The terminal of graph operation is formed by taking all the Hi’s and identifying their terminal. When Hi are all isomorphic graphs, for any positif integer n, we denote such amalgamation by G = Amal(H, v, n), where n denotes the number of copies of H and v is the terminal. The graph G is said to be an (a, d)-H-antimagic total graph if there exist a bijective function f : V (G) ∪ E(G) → {1, 2, . . . , |V (G)| + |E(G)|} such that for all subgraphs isomorphic to H, the total H-weights W(H) = ∑v∈V (H) f(v) + ∑e∈E(H) f(e) form an arithmetic sequence {a, a + d, a + 2d, ..., a + (n − 1)d}, where a and d are positive integers and n is the number of all subgraphs isomorphic to H. An (a, d)-H-antimagic total labeling f is called super if the smallest labels appear in the vertices. In this paper, we study a super (a, d)-H antimagic total labeling of connected of graph G = Amal(H, Ps+2, n) by uses a partition technique with cancelation number. The result is graph G = Amal(H, Ps+2, n) admits a super(a, d)-H antimagic total labeling for almost feasible difference d.
Co-Authors Ahmad Musyaffa' Hikamuddin Alfin Nabila Taufik Anis Nur Afni Arika Indah Kristiana Bea Hana Siswati D. Dafik Deddy Setyawan Ermita Rizki Albirri Ika Hesti Agustin, Ika Hesti Jamhari Jamhari Ridho Alfarisi Rizki Aulia Akbar Robiatul Adawiyah Susi Setiawani