THE TRIPLE IDENTITY GRAPH OF THE RING Z_n

Abstract

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