Apriantika, Retno (2017) Pelabelan graceful kuadrat dan pelabelan graceful kuadrat genap pada graph (C3*3K1,n) dan graph (K1,n:m) / Retno Apriantika. Diploma thesis, Universitas Negeri Malang.
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ABSTRAK Apriantika Retno. 2017. Pelabelan Graceful Kuadrat dan Pelabelan Graceful Kuadrat Genap Pada Graph 9001 C_3 12310 3K 12311 _(1 n) 9002 dan Graph 9001 K_(1 n) m 9002 . Skripsi Jurusan Matematika MIPA Universitas Negeri Malang. Pembimbing Prof. Drs. Purwanto Ph.D. Kata Kunci Graph Pelabelan Pelabelan Graceful Kuadrat Pelabelan Graceful Kuadrat Genap Graph 9001 C_3 12310 3K 12311 _(1 n) 9002 Graph 9001 K_(1 n) m 9002 . Suatu graph G(V E) dengan banyaknya sisi q dikatakan graph graceful kuadrat jika ada suatu fungsi injektif dari himpunan titik ke himpunan 0 1 2 q 2 sedemikian sehingga menginduksi pemetaan bijektif dari himpunan sisi ke himpunan 1 4 9 q 2 dimana sisinya mendapat label harga mutlak dari selisih pelabelan kedua titik yang terhubung langsung. Terdapat variasi baru dari pelabelan graceful kuadrat yaitu pelabelan graceful kuadrat genap. Pada skripsi ini ditemukan hasil baru yaitu graph 9001 C_3 12310 3K 12311 _( 1 n) 9002 untuk n 8805 2 adalah graph graceful kuadrat dan graph graceful kuadrat genap. Selain itu akan dibuktikan graph 9001 K_(1 n) m 9002 dengan definisi pelabelan titik dan sisi yang berbeda dari literatur adalah graph graceful kuadrat serta akan dibuktikan bahwa graph 9001 K_(1 n) m 9002 memenuhi pelabelan graceful kuadrat genap. Pembuktian dilakukan dengan cara menentukan fungsi pelabelan titik kemudian membuktikan fungsi pelabelan titiknya injektif dan fungsi pelabelan sisi yang diinduksi oleh fungsi pelabelan titik adalah pemetaan bijektif. Dari pembahasan diperoleh bahwa graph 9001 C_3 12310 3K 12311 _( 1 n) 9002 untuk n 8805 2 dan graph 9001 K_(1 n) m 9002 dapat dikenakan pelabelan graceful kuadrat dan pelabelan graceful kuadrat genap. Pelabelan graceful kuadrat dan pelabelan graceful kuadrat genap dikerjakan dengan melabeli titik terlebih dahulu kemudian dilanjutkan dengan melabeli sisi. ABSTRACT Apriantika Retno. 2017. Square Graceful Labeling and Even Square Graceful Labeling on The Graph 9001 C_3 12310 3K 12311 _( 1 n) 9002 and Graph 9001 K_(1 n) m 9002 . Minithesis Department of Mathematics Faculty of Mathematic and Natural Science State University of Malang. Advisors Prof. Drs. Purwanto Ph.D. Key words Graph Labeling Square Graceful Labeling Even Square Graceful Labeling The Graph 9001 C_3 12310 3K 12311 _(1 n) 9002 The Graph 9001 K_(1 n) m 9002 . A graph G(V E) with q edges is said to be a square graceful graph if there exists an injection function from the set of vertices to 0 1 2 q 2 such that induced a bijection mapping from the set of edges to 1 4 9 q 2 with the edge label is the absolute value of the difference between the labeling of two adjacent vertices. There is a new variation of square graceful labeling that is an even square graceful labeling. In this minithesis has found new results that the graph 9001 C_3 12310 3K 12311 _(1 n) 9002 for n 8805 2 is a square graceful graph and also an even square graceful graph. In addition here will be proved that the graph 9001 K_(1 n) m 9002 with the definition of different vertex and edge labeling function from the literature is square graceful graph and here will be proved that the graph 9001 K_(1 n) m 9002 is an even square graceful labeling. The proof has done by determining vertex labeling function and then proving that the vertex labelings function is an injection and proving that the edge labelings function are induced by vertex labelings function is a bijection mapping. From the discussion it was obtained the graph 9001 C_3 12310 3K 12311 _(1 n) 9002 for n 8805 2 and graph 9001 K_(1 n) m 9002 that can be used for square graceful labeling and even square graceful labeling. The square graceful labeling and even square graceful labeling is done by labeling the vertex first and then proceed with the edge label.
| Item Type: | Thesis (Diploma) |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Fakultas Matematika dan IPA (FMIPA) > Departemen Matematika (MAT) > S1 Matematika |
| Depositing User: | library UM |
| Date Deposited: | 14 Jun 2017 04:29 |
| Last Modified: | 09 Sep 2017 03:00 |
| URI: | http://repository.um.ac.id/id/eprint/17480 |
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