Non-superfluous intersection graph of ideals a ring

Abstract

Let R be a commutative ring with unity. The non-superfluous intersection

graph of ideals of R, denoted by G(R), is the graph whose vertex set is the

collection of non-trivial ideals of R and any two vertices, say I and J, are

adjacent if and only if I∩J is non-superfluous. The connectedness of G(R)

is studied in this paper. The notion of clique, colorability, independence

number, domination number are also established. Eventually we initiate

the concept of traversability and planarity in G(Z_n). The principal part

of this paper is to point out the role of the non-superfluous intersection

graph in Z_n.