Graf Prime Ideal Sum atas Ring Komutatif

Aldy Alie Darmawan, Dr. Sutopo, S.Si., M.Si.

2026 | Skripsi | MATEMATIKA

Diberikan suatu ring komutatif dengan elemen satuan R. Graf prime ideal sum atas ring R, dinotasikan PIS(R), adalah graf dengan simpul-simpul ideal nontrivial dari R serta dua ideal berbeda I dan J bertetangga jika I+J merupakan ideal prima. Pada skripsi ini, akan dikaji hubungan teori graf dengan teori ring melalui definisi graf PIS(R). Beberapa sifat yang akan dibahas meliputi keterhubungan graf, girth dan bilangan dominasi dari graf, serta homomorfisma graf. Lebih lanjut, akan dipelajari pula sifat-sifat dari PIS(Zn).

Let R be a commutative ring with unity. The prime ideal sum graph of R, denoted by PIS(R), is a graph whose vertices are the nontrivial ideals of R, where two distinct ideals I and J are adjacent if their sum I + J is a prime ideal. In this undergraduate thesis, we investigate the relationship between graph theory and ring theory through the definition of the PIS(R) graph. Several graph properties are studied, including connectivity, girth, domination number, and graph homomorphisms. Furthermore, the properties of PIS(Zn) are also examined.

Kata Kunci : graf prime ideal sum, teori graf, teori ring, ideal prima, graf aljabar