Indeks Eksentrisitas Zagreb Pertama dan Kedua Graf Koprima dari Grup Matriks Upper Unitriangular atas Ring Bilangan Bulat Modulo Prima

Muhammad Aris Abdillah (Universitas Islam Negeri Maulana Malik Ibrahim Malang, Indonesia)
Dewi Ismiarti (Universitas Islam Negeri Maulana Malik Ibrahim Malang, Indonesia)

Jurnal Riset Mahasiswa Matematika
Vol 2, No 2 (2022): Jurnal Riset Mahasiswa Matematika

The coprime graph of a group G is a graph Γ_G with G is its set of vertices and any two distinct vertices are adjacent if and only if their order are relatively prime. Let p be a prime number, then G_p denotes the multiplicative group of 2×2 upper unitriangular matrices over ring of integers modulo p. The purposes of this research are to study the coprime graph Γ_(G_p ) and find the first and the second Zagreb eccentricity indices of Γ_(G_p ) for p≥3. The results of this research are as follows. First Zagreb eccentricity index of coprime graph Γ_(G_p )isE_1 (Γ_(G_p ))=4p-3. Second Zagreb eccentricity index of coprime graph Γ_(G_p )isE_2 (Γ_(G_p ))=2p-2.