Judul: Pelabelan Komposit Pada Tree, Cycle, dan Graf Tangga.
Abstrak: Suatu Graf G dapat dikatakan memiliki pelabelan komposit jika graf tersebut memenuhi fungsi bijektif f:(V(G)UE(G))→{1,2,3,…,m+n} dan gcd⁡(f(uv),f(vw))≠1 dengan n adalah banyaknya verteks, m banyaknya sisi, dan u,v,w∈V(G). Graf yang memiliki pelabelan komposit disebut graf komposit. Dalam karya ilmiah ini, akan ditunjukan bahwa tree, cycle, dan graf tangga memiliki pelabelan komposit., A Graph G=(V(G),E(G)) can be said to have composite labeling if the graph fulfills the function of f:(V(G)UE(G))→{1,2,3,…,m+n} and gcd⁡(f(uv),f(vw))≠1 with order n, size m, and u,v,w∈V(G). A graph that admits composite labelling is know as a composite graph. This papper shows that the tree, cycle, and the ladder graph have composite labeling.
Keyword: Tree, cycle, Ladder graph, Composite Labeling

Judul: Pelabelan Properly Harmonis Genap pada Graf Path dan Graf yang Memuat Dua atau Tiga Caterpillar
Abstrak: Suatu fungsi 𝑓��� dikatakan sebagai pelabelan properly harmonis genap dari suatu graf 𝐺��� dengan 𝑞��� sisi jika 𝑓��� merupakan fungsi injektif dari himpunan simpulsimpul di 𝐺��� ke himpunan bilangan intejer dari 0 sampai 2𝑞��� − 1 dan fungsi 𝑓���∗ merupakan fungsi bijektif dari himpunan sisi-sisi di 𝐺��� ke himpunan bilangan intejer 0, 2, 4, … , 2(𝑞��� − 1) yang didapat dari penjumlahan dua label simpul yang insiden dengan sisi-sisinya dalam modulo 2𝑞���. Karya ilmiah ini akan menunjukkan bahwa graf path berorder 𝑚��� sebanyak 𝑛��� dan graf tak terhubung yang memuat dua atau tiga caterpillar memiliki pelabelan properly harmonis genap.
Keyword: graf caterpillar, graf path, pelabelan graf, pelabelan properly harmonis genap

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