Judul: Game Coloring Number Suatu Graf
Abstrak: Pewarnaan pada graf terdiri atas tiga macam pewarnaan yaitu pewarnaan simpul, pewamaan sisi, dan pewarnaan bidang. Coloring game merupakan salah satu permainan pewarnaan simpul yang dilakukan oleh dua orang pemain. Game chromatic number dan game coloring number merupakan nilai yang dapat dicari dari permainan coloring game. Dalam penelitian ini dibuktikan tiga teorema. Pertama, jika terdapat graf sembarang maka nilai game coloring number graf tersebut lebih besar atau sama dengan nilai game chromatic number-nya. Kedua, untuk sembarang graf dengan dua subgraf, nilai game coloring number graf kurang dari atau sama dengan nilai game coloring number subgraf pertama ditambah dengan nilai maximum degree subgraf kedua. Ketiga, untuk sembarang graf yang memiliki subgraf, nilai game coloring number subgraf kurang dari atau sama dengan nilai dari game coloring number graf tersebut.
Keyword: Coloring, Coloring game, Game chromatic number, Game coloring number, Graph theory, Teori graf, Permainan graf, Teorema

Judul: Sifat-sifat Pewarnaan Graf dan Pewarnaan Peta Provinsi Jawa Barat
Abstrak: Pewarnaan simpul pada graf adalah mewarnai simpul pada suatu graf dimana simpul yang saling adjacent diwarnai dengan warna yang berbeda. Pewarnaan simpul pada graf dapat diaplikasikan pada proses pewarnaan peta. Pada karya ilmiah ini dibahas sifat-sifat pewarnaan graf berdasarkan beberapa teorema yang salah satunya dikenal sebagai teorema Brooks. Untuk suatu ilustrasi, teorema Brooks juga diterapkan pada proses pewarnaan peta provinsi Jawa Barat berdasarkan algoritma Greedy. Dari kajian ini menunjukan bahwa graf hasil konversi peta provinsi Jawa Barat merupakan graf terhubung yang tak lengkap dan memiliki derajat simpul maksimal bernilai 7 (tujuh). Selanjutnya, peta provinsi Jawa Barat dapat diwarnai dengan empat warna, sesuai dengan teorema brooks bahwa wilayah yang bertetangga pada peta diwarnai dengan warna yang berbeda., The coloring of the vertices of a graph is coloring the vertices of the graph where adjacent vertices are colored using different colors. The coloring of vertices of a graph can be applied to the map coloring process. In this manuscript, properties of graph coloring are discussed based on theorems which one of those called as Brooks theorem. For an illustration, Brooks theorem is also applied to the map coloring of West Java province using the Greedy algorithm. This study shows that the resulting graph from the map conversion of West Java province is an incomplete connected graph and has a maximum vertex degree of 7 (seven). Furthermore, The map of West Java province can be colored with four colors, comply to Brooks theorem where neighboring regions on the map are colored in different colors.
Keyword: Brooks theorem, chromatic number, greedy algorithm, graph coloring, maximum vertex degree

Judul: Transformation of jatropha seeds (Jatropha curcas L.)  into biodiesel by in situ transesterification
Abstrak: Biodiesel is defined as mono-alkyl esters from transesterification reaction of triglycerides with alkyl alcohol. In situ transesterification is a method to produce biodiesel from oil sources of material by eliminating process steps of oil extraction and refining. The purpose of this research is to study the transformation process of Jatropha seeds into biodiesel by in situ transesterification on the 10 liters scale by studying the influence of reaction time, stirring speed and ratio methanol/hexane/material on the yield and quality of biodiesel. In situ transesterification of Jatropha seeds was carried out under the following process condition: the moisture content of Jatropha seeds were less than 2%, the particles size were ± 20 mesh and KOH concentration was 0.075 mol/L methanol. Operating condition of in situ transesterification was varied at 4 and 6 hours reaction time, 200 and 600 rpm stirring speed and ratio methanol/hexane/material (v/v/w) were 3:3:1, 4:2:1 and 5:1:1. Analysis of variance showed that reaction time, stirring speed and ratio methanol/hexane/material did not significantly affected the yield, acid value, saponification value, ester value, viscosity and ash content of biodiesel. The biodiesel yield was produced between 82.54-87.57%. The best biodiesel yield on all of treatments was 87.57% with condition treatment were reaction time of 6 hours, stirring speed 600 rpm and ratio methanol/hexane/material (v/v/w) of 4:2:1. Acid value, saponification value and ester value of biodiesel were 0.20-0.26 mg KOH/g, 185.49-194.30 mg KOH/g and 185.29-194.10 mg KOH/g respectively. Viscosity of biodiesel was 3.49-6.36 cSt. The ash content of biodiesel was 0%, but the condition treatment, were reaction time of 4 hours, stirring speed of 600 rpm and ratio methanol/hexane/material (v/v/w) of 5:1:1, had ash content of 0.007%. Jatropha cakes had total volatile matter content 1.80-3.64% and extracted material content 3.94-11.42%.
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