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"ABC Training Center (ATC) adalah suatu organisasi yang memfasilitasi pembelajaran personal dalam suatu kelompok pembelajaran yang dilengkapi dengan materi pendukung pelatihan sesuai topic pelatihan. ATC menghadapi dua masalah terpenting dalam perusahaan, yaitu system manajemen biaya tradisional dan materi pendukung pelatihan. Dalam penelitian ini, Activity-Based Management (ABM) akan menjadi sebuah alternative dalam manajemen biaya perusahaan dengan tujuan perusahaan dapat menghitung biaya pelatihan dengan lebih tepat dan akurat, terutama dalam perhitungan biaya overhead. Sistem ABM telah dikembangkan untuk memberikan sebuah representasi dari peran kegiatan-kegiatan operasional dalam pelatihan dengan lebih akurat. Sistem ABM menjadikan aktifitas dalam pelatihan serta pengaruh kegiatan tersebut dalam biaya pelatihan (Gupta & Galloway, 2003). Materi pendukung pelatihan di ATC tidak terintegrasi dan tidak mendukung untuk materi Olimpiade Matematika. Dalam thesis ini, peneliti akan menggunakan sebuah journal Mathematics Graph Labeling (MGL) (A. Parestu, 2008) sebagai materi pelatihan yang baru untuk mendukung materi Olimpiade Matematika saatini.

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ABC Training Center (ATC) is an organizational environment that facilities individual learning in group with training package supported materials based on the subject of training project. The two problems of ATC that will be researched are traditional cost management system and existing training package support materials. In this research, Activity-Based Management (ABM) will be an alternative cost management in order to accurately calculate training project costs, especially overhead costs. ABM system was developed to provide a more accurate representation of activities performed in the training project actually its cost. ABM systems examine training activities to determine their effects on costs (Gupta & Galloway, 2003). ATC training packages support materials is not well integrated and not support Olympiad curriculum theory. In this research, researcher will use a mathematics Olympiad subject: Mathematics Graph Labelling (A. Parestu, 2008) as a new alternative training package support material in ATC training package. By viewing an ABM system as an enabler to improve the ATC training operations decision-making and using Mathematics Graph Labeling as an integrated materials to improve the ATC training support materials quality and competitiveness, researcher will give results that these systems enable an operations manager to enhance the quality of ATC training package."

"ABC Training Center (ATC) adalah suatu organisasi yang memfasilitasi pembelajaran personal dalam suatu kelompok pembelajaran yang dilengkapi dengan materi pendukung pelatihan sesuai topic pelatihan. ATC menghadapi dua masalah terpenting dalam perusahaan, yaitu system manajemen biaya tradisional dan materi pendukung pelatihan. Dalam penelitian ini, Activity-Based Management (ABM) akan menjadi sebuah alternative dalam manajemen biaya perusahaan dengan tujuan perusahaan dapat menghitung biaya pelatihan dengan lebih tepat dan akurat, terutama dalam perhitungan biaya overhead. Sistem ABM telah dikembangkan untuk memberikan sebuah representasi dari peran kegiatan-kegiatan operasional dalam pelatihan dengan lebih akurat. Sistem ABM menjadikan aktifitas dalam pelatihan serta pengaruh kegiatan tersebut dalam biaya pelatihan (Gupta & Galloway, 2003). Materi pendukung pelatihan di ATC tidak terintegrasi dan tidak mendukung untuk materi Olimpiade Matematika. Dalam thesis ini, peneliti akan menggunakan sebuah journal Mathematics Graph Labeling (MGL) (A. Parestu, 2008) sebagai materi pelatihan yang baru untuk mendukung materi Olimpiade Matematika saat ini.

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ABC Training Center (ATC) is an organizational environment that facilities individual learning in group with training package supported materials based on the subject of training project. The two problems of ATC that will be researched are traditional cost management system and existing training package support materials. In this research, Activity-Based Management (ABM) will be an alternative cost management in order to accurately calculate training project costs, especially overhead costs. ABM system was developed to provide a more accurate representation of activities performed in the training project actually its cost. ABM systems examine training activities to determine their effects on costs (Gupta & Galloway, 2003). ATC training packages support materials is not well integrated and not support Olympiad curriculum theory. In this research, researcher will use a mathematics Olympiad subject: Mathematics Graph Labelling (A. Parestu, 2008) as a new alternative training package support material in ATC training package. By viewing an ABM system as an enabler to improve the ATC training operations decision-making and using Mathematics Graph Labeling as an integrated materials to improve the ATC training support materials quality and competitiveness, researcher will give results that these systems enable an operations manager to enhance the quality of ATC training package."

"Misalkan graf G(V,£), sering ditulis sebagai G, terdiri dari himpunan tak kosong simpul V dan himpunan busur £. Penambahan busur pada graf Tangga L, (n= 2) yang diperluas, akan mengakibatkan diperolehnya suatu graf baru. Graf Tangga L, (n = 2) adalah hasil perkalian Cartesius graf lintasan P, x P,. Pada tesis ini dipelajari variasi dua graf tangga yaitu : graf Tangga Segitiga LS, dan graf Tangga Segitiga Variasi X,,. Pelabelan harmonis sesuai dari definisi Graham dan Sloane (1980) adalah fungsi injektif f:V(G)—>Z,;, yang menginduksi fungsi pelabelan busur bijektif f* : E(G)— Z, dimana f*(xy) = f(x) + f(y)(mod |E|). Pada tesis ini dibuktikan bahwa graf LS, dan graf X,, untuk n = 2 merupakan graf harmonis.

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Let G(V,£), in short G, be a graph which consists of a non empty set of vertices Vand a set of edges &. By adding several edges in Ladder graph L,,(n = 2), we can obtain a new graph. A Ladder graph L,,(n = 2) is a graph product between two paths P,; X P,. In this tesis, we study on the construction of harmonious labeling of Triangular Ladder graph LS,, and Variation of Trianguler Ladder graph X,- A harmoniuous labeling, referred to Graham and Sloane ( 1980 ), is an injective function f:V(G) > Zz, which will induced bijection edge function f*:E(G) > Zg where f*: E(xy) > f(x) + fF”) (mod |E|). In this tesis, it will be proved that graph LS,, and graph X, for n => 2 is harmoniuous graphs."