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: 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: Extracellular Expression of thermostable Geobacillus stearothermophilus T1.2RQ Lipase for Biodiesel Production
Abstrak: The extracellular expression of enzymes in an excellent secretion host such as Bacillus subtilis is a useful strategy for making enzymes of industrial significance more affordable by lowering the cost of its downstream processing. Lipases are a category of hydrolases that catalyze the hydrolysis of triglycerides to glycerol and free fatty acids. Also, lipases catalyze the hydrolysis and transesterification of other esters as well as the synthesis of esters. They can perform very specific biotransformation reactions and are widely used in food, organic synthesis, detergents, cosmetic, and pharmaceutical industries. Geobacillus stearothermophilus T1.2RQ lipase is an industrially-desired thermostable lipolytic enzyme with an excellent hydrolytic and transesterification activity. This study aimed to express T1.2RQ lipase, in B. subtilis WB800 and ensure its secretion into the extracellular medium. Three signal peptides (AmyQ, Epr, LipA) and two promoters (Pgrac01 and Pgrac100) were used in the secretory-expression of T1.2RQ lipase, based on five constructed expression vectors constructed by restriction cloning and PCR mutagenesis. Sangers sequencing was used to verify constructs to ensure they are in the correct reading frame. Recombinants vectors, pHT43 (plasmid control), pHT43-T1.2RQ, pHT43- T1.2RQ_AmyQ, pHT43-T1.2RQ_Epr, and pHT43-T1.2RQ_LipA, were transformed by electroporation into Bacillus subtilis WB800. The electroporation was successful with the optimum condition of 2500V, 200 ohms, 25µF, and 5milliseconds. Recombinant B. subtilis pHT43 (negative control) and pHT43-T1.2RQlip + signal peptides were streaked on the lipidic agar, LA+TBN. All four recombinants, including the negative control (B. subtilis WB800-pHT43), produced clear zones on the TBN agar plate after overnight incubation (fig 2), indicating the presence of a lipolytic enzyme in all of the recombinant B. subtilis cells. pHT43-T1.2RQlip + signal peptides (AmyQ, Epr, and LipA) have clear zones with significantly higher diameters than B. subtilis WB800-pHT43 (negative control). This phenomenon suggests that the recombinant thermostable lipase T1.2RQ introduced into these cells was successfully expressed, thereby increasing the lipolytic capability of its host cells T1.2RQ lipase was expressed in 50ml terrific broth medium (TB) and the expression induced with 1mM IPTG. Lipase activity assay using p-nitrophenyl esters showed that all three signal peptides directed the secretion of T1.2RQ lipase into the extracellular medium. Signal peptide, LipA, resulted in the highest extracellular activity of 5.6 U/mL, which corresponds to a 6-fold increase over the parent B. subtilis WB800 strain. Meanwhile, signal peptides, AmyQ and Epr produced 4.2 U/mL and 3.4 U/mL activity respectively. SDS-Zymogram analysis confirmed that T1.2RQ lipase was correctly processed and secreted in its original size of 44 kDa. An attempt to further increase lipase expression level by promoter optimization showed that, contrary to expectation, promoter Pgrac100 exhibited similar expression levels as the original Pgrac01. Nevertheless, the demonstration of the successful secretion of T1.2RQ lipase in this work confirms the latter as a promising approach for the industrial production of the enzyme
Keyword: Bacillus subtilis, Expression, Extracellular, Heterologous, Lipase, Thermostable