Judul: Graf Pembagi-Nol Planar dan Tak-Planar
Abstrak: Graf pembagi-nol adalah suatu graf yang dibentuk dari himpunan pembaginol pada ring. Graf pembagi-nol terdiri atas himpunan simpul yang merupakan elemen-elemen pembagi-nol dari ring, serta dua simpul adjacent jika dan hanya jika hasil kalinya sama dengan nol. Graf pembagi-nol dapat digambarkan dalam sebuah bidang sedemikian rupa sehingga tidak ada dua sisi yang saling berpotongan. Graf pembagi-nol ini disebut sebagai graf planar. Karya ilmiah ini menjelaskan pembuktian teorema bahwa jika suatu graf pembagi-nol mempunyai graf yang isomorfik dengan graf lengkap dengan lima simpul atau graf bipartite lengkap dengan masing-masing himpunan simpul sebanyak tiga simpul, maka graf pembagi-nol ini bersifat tak-planar. Karya ilmiah ini juga membuktikan beberapa graf pembagi-nol merupakan graf planar atau tak-planar.
Keyword: ring, graf pembagi-nol, graf planar

Judul: Pelabelan Total Prima bagi Graf Roda 𝑊��𝑛�� , Graf Kipas 𝑓��𝑛�� , dan Graf Persahabatan 𝐹��𝑛�� .
Abstrak: Pelabelan total prima pada suatu graf G dengan banyaknya simpul �������� dan banyaknya sisi �������� adalah fungsi bijektif dari himpunan simpul digabung himpunan sisi yang dipasangkan ke himpunan bilangan bulat terurut dari 1 sampai �������� + ��������, sedemikian sehingga untuk setiap ��������, �������� ∈ ��������(��������); ��������(��������), ��������(��������), ��������(����������������) adalah saling prima relatif secara berpasang-pasangan. Sebuah graf yang memiliki pelabelan total prima disebut graf total prima. Dalam karya ilmiah ini, ditunjukan bahwa graf roda ���������������� , graf kipas ���������������� , dan graf persahabatan ���������������� ketiganya memiliki pelabelan total prima dan diberikan contoh pelabelan total prima bagi graf roda ����������������, graf kipas ����������������, dan graf persahabatan ����������������.
Keyword: graf kipas, graf persahabatan, graf roda, pelabelan total prima

Judul: Pengaruh Jumlah Bahan Pretanning dan Minyak Biji Karet (Hevea brasiliensis) Terhadap Mutu Kulit Samoa. Di
Abstrak: Animal hides or skins are the most valuable by product of the meat industry. Most of those hides are converted into leather by leather tanning process. Chrome based tanning is the most popular tanning process. At the chrome based tanning process, a lot of amount chrome are throw away into the environment that make a significant effect to the biological and ecological environment damaged. Due to concerns over the use and disposal of chromed tanned leather, the leather industry is now facing increasing scrutiny over its use of chrome as tanning agent. The use of non-chrome tannages has gradually become pre-eminent to producing leather, particularly in the European automotive leather markets. Chamois leather is one of leather product. It is produced from animal hides/skins by oil tanning process, usually with fish oil. High price and odour problems to the chamois leather that produced using fish oil motivate to do some research to solve that problems. Rubber seed oil is an oil that predicted can substitute fish oil. Pretanning process is needed to increase the oil penetration and protects the pelt from putrefying during oxidation periods (Khrisnan et al., 2005). Relugan GT 50 is the agent that used on this research. Relugan GT 50 is an aldehyde tanning agent, produced by BASF. This research was aimed to find out the effects of Relugan GT 50 concentration (offer) and rubber seeds (Hevea brasiliensis) oil to the chamois leather’s quality. Beside that, this research is also aimed to decide the best combination of the factors to produce chamois leather also to know the chamois leather characteristics. The preliminary research was carried out by analyzing the rubber seed’s kernel and eggshell as well as physico-chemical properties of the rubber seed oil. The main research was done by tanning the skin with Relugan GT 50 in concentrations of 1.5, 3.0 and 4.5% followed by rubber seed oil concentrations of 10, 20, and 30%. The experimental design used was completely randomize factorial design. The preliminary research shows that rubber seed’s kernel was 49% and rubber seed’s eggshell was 51%. The rubber seed’s oil characterstics were density of 0.94 (g/cm3), viscosity of 48,4 centistokes, colour of 2713 PtCo units, inodine value 113 g iod/ 100 g, peroxide value of 24 miliequivalent/1000 gram oil, acid value of 15 mg KOH/g oil and FFA content of 5.8%. The research shows that Relugan GT 50 concentration significantly affected shrinkage temperature (Ts) and pH; rubber seed oil concentration significantly affect the organoleptic properties of the leather. The optimum conditions for the tanning were Relugan GT of 3.0% concentration and 10% rubber seeds oil. The physical properties of the leather were shrinkage temperature of 75oC, thickness of 0.92 mm, tensile strength of 21.50 N/mm2, elongation at break of 144%, tear strength of 55.77 N/mm, water absorption of 266% (2 hours) and 299% (24 hours). The chemical properties were oil content of 2.5%, ash content of 1.2% and pH of 8. The organoleptic properties were softness of 7–8, colour of 8-9, and odour of 8-9.
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