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: 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
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Judul: Durability of Specific Immunoglobulin (Ig) Y Againts Influenza and Covid-19 in Sunscreen
Abstrak: The benefit of specific immunoglobulin Y (Ig Y) as an active ingredient in personal care products such as sunscreen has not been properly studied. Our study aims to evaluate the reliability of specific IgY against influenza and the COVID-19 virus in a sample sunscreen product. Specific IgY influenza and COVID-19 viruses were inserted in the sample sunscreen at two concentrations of 0.1% and 0.25%. Three treatments were observed: control (C) sunscreen without IgY, treatment 1 (T1) sunscreen with 0.1% IgY, and treatment 2 (T2) sunscreen with 0.25% IgY. Organoleptic observations were carried out to monitor changes in aroma, color, and texture, and sunscreen sampling was done every week for 6 weeks. The durability of IgY was evaluated using an enzyme-linked immunosorbent assay (ELISA) and a neutralization assay. Organoleptic observation from weeks 1 to 6 showed consistency in its aroma, color, and texture. Enzyme-linked immunosorbent assay and neutralization assay (NA) results of the T1 and T2 groups showed negative results except for sample T1 at week 5, which showed a positive result in the Influenza A ELISA. Based on the results, it seems that IgY concentrations of 0.1% or 0.25% were not optimal. However, this negative result might be due to low concentration of the IgY and the presence of beeswax, which inhibits IgY and causes it to dissolve in distilled water, thus preventing it from being detected in the assay.
Keyword: Immunoglobulin Y, Sunscreen, Influenza, COVID-19, Biological Activity