LINE GRAPH ASSOCIATED TO ORDER-CONGRUENCE GRAPH OF THE COMMUTATIVE RING Zp, p IS PRIME
The order-congruence graph of was defined as the graph whose vertices are the elements of the ring and any two distinct vertices x and y are adjacent in whenever or with where p is the order of In this paper we define the line graph of order-congruence graph of denoted by as the graph with all the edges of as vertices and any two distinct vertices are adjacent if and only if their corresponding edges share a common vertex in the graph In this paper we explore structural properties of
commutative ring, order-congruence graph, line graph.