THE TRIPLE IDENTITY GRAPH OF THE RING Z_n - Kurniawan, Vika Yugi; Ekasiwi, Chessa Fanny; Wiyono, Santoso Budi (BAREKENG: Jurnal Ilmu Matematika dan Terapan, 2025)
Let be a commutative ring with identity and is an identity element of . The triple identity graph of the ring , represented by ), is an undirected simple graph with the vertex set . In , two different vertices and is called adjacent if there is an element such that and . The triple identity graph of the ring of integers modulo , represented by , is the subject of this study. We obtain several results regarding the properties of the graph , which are summarized as follows. The graph is a connected graph if and only if is prime and . If is connected, then diam and gr. Furthermore, is a Hamiltonian graph if is a prime number and .