Judul: Pelabelan Super Edge Magic Graceful pada Graf Petersen 𝑃��(𝑛��, 1) dan 𝑃�� (𝑛��, 𝑛��−1 2 ).
Abstrak: Pelabelan edge magic graceful 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 dimulai dari 1 sampai ������ + ������, sedemikian sehingga untuk semua sisi, nilai mutlak dari penjumlahan label verteks yang saling adjacent dikurangi dengan label dari sisi yang incident dengan verteks tersebut akan sama dengan ������, ������ adalah konstanta magic. Pelabelan edge magic graceful yang memasangkan himpunan simpul ke himpunan bilangan bulat terurut {1,2, … , ������} disebut pelabelan super. Dalam karya ilmiah ini, ditunjukkan bahwa graf Petersen ������(������, 1) dan ������ (������, ������−1 2 ) keduanya memiliki pelabelan super edge magic graceful.
Keyword: graf Petersen, pelabelan super edge magic graceful

Judul: Super (a,d) edge antimagic total labeling pada graf petersen
Abstrak: Karya ilmiah ini membuktikan teorema-teorema untuk memperoleh super (a,d)-edge-antimagic total labeling pada graf petersen. Pada pelabelan, didefinisikan jumlah label sisi (edge) dan label dua simpul (vertex) yang menempel pada sisi (edge) disebut sebagai bobot sisi (edge-weights). Suatu graf yang memiliki bobot sisi yang berbeda untuk setiap sisi maka graf ini disebut graf dengan antimagic total labeling. Jika semua sisi mempunyai bobot sisi yang berbeda dan himpunan bobot sisi dari semua sisi membentuk barisan aritmatika dengan suku awal a dan beda (selisih) d maka pelabelan tersebut disebut (a,d)-edge-antimagic total labeling. Kemudian, (a,d)-edge-antimagic total labeling disebut super (a,d)-edge-antimagic total labeling jika f(v(g)) = {1, 2, …, v} dan f(e(g)) = {v+1, v+2, …, v+e}. Terdapat dua pembuktian teorema yang dibahas dalam karya ilmiah ini. Teorema pertama membuktikan bahwa graf petersen p(n,m) dengan n ≥ 3 bilangan bulat ganjil dan m = 1, memiliki super (5𝑛+52,2)-edge-antimagic total labeling. Teorema kedua membuktikan graf petersen p(n,m) dengan n ≥ 3, 1 ≤ m ˂ 𝑛2 , mempunyai sebuah super (4𝑛+2,1)-edge-antimagic total labeling
Keyword: edge-antimagic total labeling, antimagic total labeling, graf petersen, super (a,d)

Judul: Utilization of hydrolized duckweed (Lemna minor) meal as a soybean replacement in Nile tilapia (Oreochromis niloticus) diet,
Abstrak: Tilapia is a fast growing fish widely cultured in many tropical and sub tropical countries. The recent production figures reported our global production estimates for 2015 is 5,576.8 metric tons. In developing countries the major challenges facing aquaculture industry is high cost of production associated with fish feeds. Feed represents 40-70% of operating costs for aquaculture operations, increasing expenses and potential declining supplies soybean meal have led scientists to search for less expensive but compatible alternative protein sources for fish feed; most of which are based on animal or plant protein sources. The objectives of study was to determine the incubation period for hydrolysis of duckweed and to evaluate the use of hydrolized duckweed as aprotein source for the growth performance of Nile tilapia Three experiments were conducted to determine the composition and digestibility of hydrolyzed duckweed meal by sheep rumen liquor as the replacement of soybean meal in the diet of Nile tilapia. The first trial examined the effectivity of sheep rumen liquor enzyme to decrease crude fiber contents of (DWM), the added volume of sheep rumen liquor was 100 ml/kg DWM and then it was incubated for 0, 12, 24 hr . The second trial was to evaluate the apparent digestibility of hydrolyzed DWM for Nile Tilapia, apparent digestibility were determined using chromic oxide indicator added to both reference diet and test diets. The feed ingredients used in the trial were hydrolyzed DWM (HDWM) and unhydrolyzed DWM (DWM). Ten fish with an average weight of 18±0.36g were used in the trial and reared in the aquarium of size 30×40×50cm for 15 days; feces were collected from three replicates using a fecal collection column attached to the aquarium. Third trial was to evaluate the growth performance of Tilapia fed test diet with hydrolyzed Duckweed meal (HDWM). The experimental design was set according to completely randomized design with four treatments and three replicates of HDWM inclusion levels that is 0%, 15%, 30% and 45%. Nile tilapia fish with initial body weight of 18±0.36g was kept in 12 units aquarium size of 30×40×50cm at stocking density of 10fish/aquarium, the fish were fed two times a day at 08:00am and 16:00pm to apparent satiation for a period of 60 days. The results indicated that duckweed meal (DWM) hydrolyzed with 100 mL/kg and incubated for 24 hrs showed the lowest crude fiber contents of 13.68% compared to other treatments. Total digestibility of hydrolyzed duckweed (HDWM) meal was 87.3% compared with unhydrolyzed duckweed (DWM) which was 66.8%. Total final weight (TFW), survival rate (SR), specific growth rate (SGR), feed conversional rate (FCR) and protein retention (PR) shows growth performance at 15% inclusion. The results of this study showed that 100mL/kg sheep rumen liquor at incubation period of 24 hr can be suitable for hydrolysis of duckweed to reduce crude fiber also hydrolyzed duckweed can substitute soybean meal at an incubation rate of 15% in the diet of Nile tilapia and had the same growth and FCR with control diet
Keyword: Digestibility, Duckweed meal, Growth performance, Sheep rumen