Judul: Pengaruh Pemberian Sinbiotik terhadap Kinerja Produksi Udang Vaname Litopenaeus vannamei di Tambak Pinang Gading, Bakauheni, Lampung
Abstrak: Synbiotic applications on a laboratory scale had been performed and was able to improve survival rate, growth and immune response against multiple pathogens. The purpose of this research was to test the effects of synbiotic administration on production performance of white shrimp reared in shrimp ponds on field scale. Vibrio alginolyticus SKT-b bacterium and oligosaccharides extracted from sweet potato were used as probiotic and prebiotic. White shrimp that has been reared for 25 days after stocking was reared in shrimp pond 16 (2500 m2), pond 17 (3100 m2), pond 18 (4100 m2) and pond 19 (3600 m2) in stocking density of 72 shrimps/m2. This research consisted of two treatments with two replications: K treatment (without synbiotic administration) and P treatment (administration of 1% probiotic and 2% prebiotic). The results showed that synbiotic administration was able to improve the survival rate, daily growth rate, feed conversion ratio and immune response of white shrimp.
Keyword: pond, production performance, white shrimp, Synbiotic

Judul: Application of Multispesies Probiotics, Prebiotics and Synbiotics for the Prevention of Vibriosis in Vannamei Shrimp Litopenaeus vannamei
Abstrak: Salah satu masalah dalam budidaya udang adalah serangan penyakit vibriosis akibat infeksi bakteri Vibrio parahaemolyticus. Alternatif preventif dan ramah lingkungan yang dapat ditawarkan yaitu menggunakan probiotik, prebiotik dan sinbiotik. Penelitian ini bertujuan untuk menguji pengaruh pemberian multispesies probiotik Lactobacillus plantarum dan Bacillus cereus, prebiotik mannanoligosakarida serta sinbiotik terhadap kinerja pertumbuhan dan respons imun udang vaname yang diinfeksi bakteri V. parahaemolyticus. Penelitian ini terdiri atas empat perlakuan pada uji suplementasi dan lima perlakuan pada uji tantang, yaitu kontrol (tanpa suplementasi), suplementasi multispesies probiotik L. plantarum dan B. cereus, prebiotik MOS serta sinbiotik. Udang vaname dengan bobot rata-rata 0,55±0,01 g dipelihara dengan padat tebar 15 ekor/akuarium. Udang diberi pakan komersial yang telah diperkaya dengan multispesies probiotik L. plantarum dan B. cereus, prebiotik MOS serta sinbiotik selama 40 hari, kemudian diuji tantang dengan bakteri V. parahaemolyticus. Parameter yang diamati selama penelitian meliputi tingkat kelangsungan hidup, laju pertumbuhan spesifik, rasio konversi pakan, total haemocyte count, differential haemocyte count, aktivitas fagositik, aktivitas respiratory burst, dan aktivitas phenoloxidase. Hasil penelitian menunjukkan bahwa pemberian multispesies probiotik L. plantarum dan B. cereus, prebiotik MOS serta sinbiotik dapat meningkatkan kinerja pertumbuhan dan respons imun udang vaname yang diinfeksi V. parahaemolyticus dengan hasil terbaik pada perlakuan multispesies probiotik dan sinbiotik., One of the problems in shrimp farming is the attack of vibriosis disease due to infection with Vibrio parahaemolyticus bacteria. Preventive and environmentally friendly alternatives that can be offered are using probiotics, prebiotics and synbiotics. This study aimed to examine the effect of multispecies probiotics Lactobacillus plantarum and Bacillus cereus, mannanoligosaccharide prebiotics and synbiotics on growth performance and immune response of white vaname shrimp infected with V. parahaemolyticus bacteria. This study consisted of four treatments in the supplementation test and five treatments in the challenge test, namely control (without supplementation), multispecies supplementation of probiotics L. plantarum and B. cereus, MOS prebiotics and synbiotics. Vannamei shrimp with an average weight of 0.55±0.01 g were reared at a stocking density of 15 fish/aquarium. Shrimp were fed commercial feed enriched with multispecies probiotic L. plantarum and B. cereus, MOS prebiotic and synbiotic for 40 days, then challenged with V. parahaemolyticus. Parameters observed during the study included survival rate, specific growth rate, feed conversion ratio, total haemocyte count, differential haemocyte count, phagocytic activity, respiratory burst activity, and phenoloxidase activity. The results showed that the administration of multispecies probiotics L. plantarum and B. cereus, MOS prebiotics and synbiotics could improve the growth performance and immune response of white vaname shrimp infected with V. parahaemolyticus with the best results in the multispecies treatment of probiotics and synbiotics.
Keyword: Bacillus cereus, Lactobacillus plantarum, Litopenaeus vannamei, Mannanoligosaccharide (MOS), Vibrio parahaemolyticus

Judul: Cycle Hamilton pada Graf Lengkap, Graf Regular, dan Graf 2-Connected 4-Regular Berorder Kurang dari Sepuluh
Abstrak: Suatu graf disebut graf Hamilton apabila graf tersebut memuat cycle Hamilton, yaitu cycle yang melewati setiap vertex tepat satu kali. Menentukan keberadaan cycle Hamilton pada suatu graf dapat menggunakan syarat cukup yang berupa teorema-teorema yang telah diperkenalkan sejak tahun 1950-an. Beberapa syarat cukup yang dibahas dalam karya ilmiah ini adalah syarat cukup yang berhubungan dengan graf lengkap dan graf regular. Suatu graf lengkap berorder 𝑛������ ≥ 3 dan graf r-regular berorder 𝑛������ ≤ 2𝑟������ + 1 merupakan graf Hamilton, Karena kedua graf tersebut memuat cycle Hamilton. Selanjutnya, syarat cukup tersebut digunakan untuk menentukan keberadaan cycle Hamilton pada graf 2-connected 4- regular berorder kurang dari 10.
Keyword: graf Hamilton, graf regular, graf lengkap, graf 2-connected 4-regular