Judul: Beberapa Sifat pada Graf a-Vertex Consecutive Magic dan Graf b-Edge Consecutive Magic
Abstrak: Suatu pelabelan total simpul ajaib 𝜆����� dari graf 𝐺����� = (𝑉�����, 𝐸�����) dengan himpunan simpul 𝑉����� = 𝑉�����(𝐺�����) dan himpunan sisi 𝐸����� = 𝐸�����(𝐺�����) disebut pelabelan total a-vertex consecutive magic jika himpunan label dari simpul 𝐺����� adalah 𝜆�����(𝑉�����) = {𝑎����� + 1, 𝑎����� + 2, … , 𝑎����� + 𝑛�����} dengan 𝑎����� ∈ {0,1,2, … , 𝑒�����}. Pelabelan tersebut merupakan pelabelan total b-edge consecutive magic jika himpunan label dari sisi 𝐺����� adalah 𝜆�����(𝐸�����) = {𝑏����� + 1, 𝑏����� + 2, … , 𝑏����� + 𝑒�����} dengan ∈ {0,1,2, … , 𝑛�����} . Dinotasikan 𝑒����� adalah banyaknya sisi dan 𝑛����� adalah banyaknya simpul. Terdapat empat teorema yang akan dibahas dalam karya ilmiah ini. Teorema pertama menunjukkan magic constant dari graf a-vertex consecutive magic. Teorema kedua menunjukkan bahwa jika 𝐺����� adalah suatu graf a-vertex consecutive magic yang memiliki satu simpul terisolasi, maka 𝑎����� = 𝑒����� dan order 𝑛����� serta size 𝑒����� memenuhi persamaan (𝑛����� − 1)2 + 𝑛�����2 = (2𝑒����� + 1)2. Teorema ketiga menunjukkan bahwa jika 𝐺����� adalah suatu graf a-vertex consecutive magic yang memiliki order 𝑛����� dan size 𝑒����� = 𝑛����� − 1, maka 𝑛����� adalah bilangan ganjil dan 𝑎����� = 𝑛����� − 1. Teorema keempat menunjukkan magic constant dari graf b-edge consecutive magic.
Keyword: pelabelan total simpul ajaib, graf a-vertex consecutive magic, graf bedge consecutive magic

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: The use of hydrolyzed Azolla pinnata to substitute soybean meal in juvenile Nile tilapia (Oreochromis niloticus) diet
Abstrak: Nile tilapia, Oreochromis niloticus is one of the most cultured fish species in tropical and subtropical countries of the world. It provides one of the main sources of income and animal protein throughout the world. Because of their faster growth rate, tolerance to harsh environment and ease culture technique, tilapia offers the possibility of commercial and home-grown protein. However, feed is the key cost variable in tilapia culture, which accounts 80% of total production cost. The high feed cost is mostly caused by the high protein content in the diet and the high price of protein. Soybean is one of the most utilized plant protein sources in aquaculture feed. However due to its cost, availability and competitiveness with other human use, alternative plant protein sources were explored which is Azolla pinnata. Azolla pinnata is a cheap, sufficient nutritional value for protein lipid carbohydrate vitamin and mineral, locally available and affordable to most fish farmers. Nutritional quality of Azolla pinnata can be improved by fermentation methods or by hydrolysis using sheep rumen liquor. This contains protease, lipase, amylase, and cellulase enzymes. This study aimed to use hydrolyzed aquatic macrophyte Azolla pinnata meal to substitute soybean meal (SBM) in the diet of Nile tilapia (O.niloticus). Where, enhancement of nutritional composition of azolla pinnata, hydrolyzed Azolla pinnata digestibility and inclusion level of hydrolyzed Azolla pinnata in Nile tilapia diet for growth performance was evaluated. In the nutritional composition of the Azolla pinata meal after hydrolysis with rumen digestive fluid showed satisfactory increase of nutritional contents including protein content 34.03%, lipid 5.56%, and reduced crude fiber up to 7.80%. Morever chromic oxide at 0.5% was mixed as the diet inert markers. The fish feces were collected from six aquariums (50×40×30cm3) during 21 days. The reference diet showed high digestibility of dry matter, protein and energy including 88.1%, 92.8% and 91.2% respectively, for those of test diet with 34.1% 50.3% and 32.3% respectively for digestibility study. Concerning the growth study, five test diets of 30% crude protein were formulated by different substitution level of soybean meal by hydrolyzed Azolla pinnata meal including diets A, B, C, D, E (0%, 10%, 20%, 30% and 40% of hydrolyzed Azolla pinnata meal respectively). The experiment was conducted during 57 days where 10 fish of 8-10g were stocked in 15 aquariums (50×40×30cm3). Fish were fed two times daily to apparent satiation. At the end of this study, results showed that hydrolyzed Azolla pinnata meal can be added to Nile tilapia feed up to 30% without affecting fish growth performance.
Keyword: Digestibility, growth, hydrolyzed Azolla pinnata, Oreochromis niloticus