Pelabelan total busur ajaib b-busur berurutan pada graf lobster semi teratur Ln (r,0; 1,r) dan Ln (r,0; 1,s) = A b-edge consecutive edge magic total labeling on semi regular lobster graph (r,0; 1,r) and Ln (r,0; 1,s)
| Main Author: | Sri Wahyuni Wulandari, author |
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| Format: | Bachelors |
| Terbitan: |
Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Indonesia
, 2012
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| Subjects: | |
| Online Access: |
http://lib.ui.ac.id/file?file=digital/20310323-S43071-Pelabelan total.pdf |
Daftar Isi:
- [<b>ABSTRAK</b><br> Misalkan suatu graf G = (V, E) dengan v = |V| simpul dan e = |E| busur adalah graf berhingga, sederhana, dan tidak berarah. Pelabelan total busur ajaib pada 𝐺 adalah pemetaan bijektif f dari 𝑉∪𝐸 ke himpunan bilangan bulat 1,2,3,?,𝑣+𝑒 , dimana terdapat suatu konstanta 𝑘 sedemikian sehingga bobot busur 𝑤𝑓 𝑥𝑦 =𝑓 𝑥 +𝑓 𝑥𝑦 +𝑓 𝑦 =𝑘 untuk setiap 𝑥𝑦∈𝐸. Jika 𝑓 adalah suatu pelabelan total busur ajaib dari G dan 𝑓 𝐸 = 𝑏+1,𝑏+2,𝑏+3,?,𝑏+𝑒 ,0≤𝑏≤𝑣 maka 𝑓 adalah pelabelan total busur ajaib b-busur berurutan. Pada makalah ini diberikan konstruksi pelabelan total busur ajaib b-busur berurutan pada salah satu kelas graf pohon, yaitu graf lobster semi reguler 𝐿𝑛 𝑟,0;1,𝑟 dan 𝐿𝑛 𝑟,0;1,𝑠 dengan 𝑛,𝑟, dan 𝑠 adalah bilangan-bilangan bulat positif. <hr> <b>ABSTRACT</b><br> Let G = (V, E) be a finite, simple, and undirected graph with v = |V| vertices and e = |E| edges. An edge magic total labeling of G is a bijection f from 𝑉∪𝐸 to the set of consecutive integers 1,2,3,?,𝑣+𝑒 , where there is a constant 𝑘 such that 𝑤𝑓 𝑥𝑦 =𝑓 𝑥 +𝑓 𝑥𝑦 +𝑓 𝑦 =𝑘 for all 𝑥𝑦∈𝐸. If 𝑓 is an edge magic total labeling of G and 𝑓 𝐸 = 𝑏+1,𝑏+2,𝑏+3,?,𝑏+𝑒 ,0≤𝑏≤𝑣, then 𝑓 is an b-edge consecutive edge magic total labeling. In this skripsi will be given constructions of b-edge consecutive magic total lebeling for a class of tree graph, that is semi regular lobster graph 𝐿𝑛 𝑟,0;1,𝑟 and 𝐿𝑛 𝑟,0;1,𝑠 with 𝑛,𝑟, and 𝑠 are positive integers., Let G = (V, E) be a finite, simple, and undirected graph with v = |V| vertices and e = |E| edges. An edge magic total labeling of G is a bijection f from 𝑉∪𝐸 to the set of consecutive integers 1,2,3,?,𝑣+𝑒 , where there is a constant 𝑘 such that 𝑤𝑓 𝑥𝑦 =𝑓 𝑥 +𝑓 𝑥𝑦 +𝑓 𝑦 =𝑘 for all 𝑥𝑦∈𝐸. If 𝑓 is an edge magic total labeling of G and 𝑓 𝐸 = 𝑏+1,𝑏+2,𝑏+3,?,𝑏+𝑒 ,0≤𝑏≤𝑣, then 𝑓 is an b-edge consecutive edge magic total labeling. In this skripsi will be given constructions of b-edge consecutive magic total lebeling for a class of tree graph, that is semi regular lobster graph 𝐿𝑛 𝑟,0;1,𝑟 and 𝐿𝑛 𝑟,0;1,𝑠 with 𝑛,𝑟, and 𝑠 are positive integers.]