Pelabelan graceful kuadrat dan pelabelan graceful kuadrat genap pada graph (C3*3K1,n) dan graph (K1,n:m) / Retno Apriantika

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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Abstract

ABSTRAK Apriantika, Retno. 2017. Pelabelan Graceful Kuadrat dan Pelabelan Graceful Kuadrat Genap Pada Graph 〈C_3*〖3K〗_(1,n) 〉 dan Graph 〈K_(1,n):m〉. 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 〈C_3*〖3K〗_(1,n) 〉, Graph 〈K_(1,n):m〉. 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,ÔǪ,q^2} sedemikian sehingga menginduksi pemetaan bijektif dari himpunan sisi ke himpunan {1,4,9,ÔǪ,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 〈C_3*〖3K〗_( 1,n) 〉 untuk n≥2 adalah graph graceful kuadrat dan graph graceful kuadrat genap. Selain itu akan dibuktikan graph 〈K_(1,n):m〉 dengan definisi pelabelan titik dan sisi yang berbeda dari literatur adalah graph graceful kuadrat, serta akan dibuktikan bahwa graph 〈K_(1,n):m〉 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 〈C_3*〖3K〗_( 1,n) 〉 untuk n≥2 dan graph 〈K_(1,n):m〉 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 〈C_3*〖3K〗_( 1,n) 〉 and Graph 〈K_(1,n):m〉. 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 〈C_3*〖3K〗_(1,n) 〉, The Graph 〈K_(1,n):m〉. 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,ÔǪ,q^2} such that induced a bijection mapping from the set of edges to {1,4,9,ÔǪ,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 〈C_3*〖3K〗_(1,n) 〉 for n≥2 is a square graceful graph and also an even square graceful graph. In addition, here will be proved that the graph 〈K_(1,n):m〉 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 〈K_(1,n):m〉 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 〈C_3*〖3K〗_(1,n) 〉 for n≥2 and graph 〈K_(1,n):m〉 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) > Jurusan Matematika (MAT) > S1 Matematika
Depositing User: Users 2 not found.
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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