Judul: Ongkos irregularitas sebuah graf
Abstrak: Tulisan ini mengkaji bagaimana cara mcngubah sualu graf menjadi graf yang irregular, yaitu dengan menambahkan beberapa edge pacta graf asal. Untuk sebuah graf G, didefinisikan ongkos irregularitas ic(G) yaitu jumlah minimum tambahan edge sedemikian sehingga menjadi Multigraf H yang merupakan multigraf G irregular. Akan ditentukan ongkos irregularitas dari graf regular, graf mendekati regular, dan graf mendekati irregular.
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Judul: Pelabelan Super Edge-Magic dan Super Vertex-Antimagic pada Graf Kipas, Graf Matahari, Graf Ulat, dan Graf Prisma.
Abstrak: Pelabelan edge-magic dan vertex-antimagic pada suatu graf dengan banyaknya simpul dan banyaknya sisi adalah fungsi bijektif dari himpunan simpul digabung himpunan sisi yang dipasangkan ke himpunan bilangan bulat terurut 1,2, … , �� + �� , sedemikian sehingga semua bobot sisi mempunyai nilai yang sama dan semua bobot simpulnya mempunyai nilai yang berbeda. Pelabelan edge-magic dan vertex-antimagic yang memasangkan himpunan simpul ke himpunan bilangan bulat terurut 1,2, … , disebut pelabelan super. Dalam karya ilmiah ini, akan ditunjukkan bahwa graf kipas, graf matahari, graf ulat, dan graf prisma memiliki pelabelan super edge-magic dan super vertex-antimagic.
Keyword: graf kipas, graf matahari, graf prisma, graf ulat, pelabelan super edgemagic total, pelabelan super vertex-antimagic total, pelabelan total

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