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: Coloring Covid-19 Map Based on Fuzzy Directed Graph
Abstrak: Pewarnaan graf merupakan salah satu aplikasi dalam teori graf dengan mewarnai verteks suatu graf dimana verteks yang adjacent diberi warna yang berbeda. Salah satu aplikasi pewarnaan graf adalah pewarnaan peta. Pada karya ilmiah ini dibahas pewarnaan peta kasus COVID-19 di Indonesia menggunakan graf berarah fuzzy. Tiap provinsi bertindak sebagai verteks dan sisi berarah yang terhubung antara dua verteks ada jika terdapat riwayat perjalanan antara satu provinsi ke provinsi lain. Pewarnaan graf berarah fuzzy mengikuti algoritma Mahapatra. Dari kajian ini ditunjukkan bahwa indeks kromatik dari hasil pewarnaan graf berarah fuzzy pada kasus COVID-19 di Indonesia terdiri dari dua warna dasar minimum yang dibutuhkan graf setelah seluruh verteks diwarnai dengan nilai minimum 1,463., Graph coloring is one of the applications in graph theory by coloring the vertices of a graph where adjacent vertices are given different colors. One of the applications of graph coloring is map coloring. In this manuscript, the coloring of maps of COVID-19 cases in Indonesia using directed fuzzy graphs. Each province acts as a vertex and there exists a directed edge connected between two vertices if there is a history of travel between one province to another. The coloring of the directed fuzzy graph is based on Mahapatra's algorithm. This study shows that the chromatic index of the directed fuzzy graph coloring result in the case of COVID-19 in Indonesia consists of two minimum base colors required by the graph after all vertices are colored and the minimum value is 1,463.
Keyword: chromatic number, directed fuzzy graph, graph coloring, map coloring

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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