Judul: k, d)-graceful Labeling on 𝑇𝑃 -tree and Subdivision of 𝑇𝑃 -tree.
Abstrak: Karya ilmiah ini membuktikan bahwa setiap 𝑇𝑃 -tree dan subdivisi dari 𝑇𝑃 -tree dapat dilabeli dengan pelabelan (k, d)-graceful untuk setiap bilangan bulat positif k dan d. Pelabelan (k, d)- graceful pada suatu graf adalah pelabelan graceful yang simpulnya dapat dilabeli dengan bilangan bulat, sehingga himpunan simpulnya dipetakan ke 0, 1, 2, … , 𝑘 + 𝑞 − 1 𝑑 dan himpunan sisinya dipetakan ke {𝑘, 𝑘 + 𝑑, 𝑘 + 2𝑑, … , 𝑘 + 𝑞 − 1 𝑑}, dengan 𝑞 adalah banyaknya sisi pada suatu graf. Terdapat dua teorema dan satu akibat yang dibahas dalam karya ilmiah ini. Teorema pertama membuktikan bahwa setiap 𝑇𝑃 -tree dapat dilabeli dengan pelabelan (k, d)-graceful. Teorema ini mengakibatkan suatu pernyataan bahwa pelabelan (k, d)-graceful merupakan pelabelan (k, d)- balanced. Teorema kedua membuktikan bahwa subdivisi dari 𝑇𝑃 -tree dapat dilabeli dengan pelabelan (k, d)-graceful
Keyword: 

Judul: Tree berdiameter lima adalah graceful
Abstrak: This manuscript presents some proofs that every tree of diameter five is graceful. A graceful tree is a graph which has a graceful labelling. This labelling assigns absolute difference of connected vertices, such that the resulting edge labels are mutually distinct. There are three theorems to be considered. First theorem proves that every tree of diameter four is graceful. Second theorem proves that every tree of diameter five is graceful or nearly graceful. The third theorem improves the second theorem and shows that every tree of diameter five is nearly graceful, which can be transformed into graceful using some certain patterns.
Keyword: Graf, Pelabelan graceful, Bogor Agricultural University, Institut Pertanian Bogor, IPB

Judul: Effectiveness of Microwave Oven against B. cereus to Reach Food Safety Objective in Cook-chill Foods
Abstrak: Cook-chill foods are meal that being cooked and then chilled quickly until further consumption. Usually before being consumed, the foods are reheated by the consumers to improve the organoleptic property and also to destroy bacteria. One of the things that need to be considered is that cook-chill foods that are originated from grains like rice or wheat are vulnerable to be contaminated by pathogen, especially Bacillus cereus. Another problem is that on the packaging of specific cook-chill food that being investigated, there is only instruction manual on how to reheat the food with 1800 W microwave oven. Microwave oven that is being used in household level is usually lower than 1000 W, so there is a possibility under-cooking may happen because there is no standardization on how to heat food with microwave on household level. The research was conducted in five steps, which were; (1) investigation of standard plate count and B. cereus count on two cook-chill foods (spaghetti bolognaise and black pepper chicken rice), (2) challenge test on those cook-chill foods to evaluate the growth of B. cereus on cook-chill food on 15oC, (3) challenge test to evaluate inactivation of vegetative cells and spores of B. cereus by microwave oven (850 watt and 410 watt), (4) to evaluate if FSO of those cook-chill foods could be achieved based on data gathered in the previous results, and (5) to study the effect of microwave oven and moist heat against leakages of nucleic acids and proteins of B. cereus. The results of this research were that microwave oven with 850 watt power could still reach food safety objective (FSO) when cook-chill foods were being reheated for the recommended time on the packagings (45 seconds for spaghetti bolognaise and 2 minutes for black pepper chicken rice), however when using 410 watt microwave oven, FSO could not be achieved. The mechanism of which why microwave oven could destroy vegetative cell and spores of B. cereus was also investigated. The result was that heat treatment using microwave oven differed when compared to moist heat since heat treatment using microwave oven caused leakages of nucleic acid and protein content of the vegetative cells and spores of B. cereusin much larger effect than moist heat.
Keyword: cook-chill foods, Bacillus cereus, microwave, rice, spaghetti, food safety objective