In this paper, a new kind of graph on a commutative ring R with identity, namely the co-
maximal ideal graph is defined and studied. We use to denote this graph, with its vertices the …

Let R be a commutative ring with identity. The maximal graph of R is the graph whose
vertices are elements of R, where two distinct vertices x and y are adjacent if and only if …

Let R be a commutative ring R with 1. In [PK Sharma, SM Bhatwadekar, A note on graphical
representation of rings, J. Algebra 176 (1995) 124–127], Sharma and Bhatwadekar defined …

Let R be a commutative ring with identity. The essential ideal graph of R, denoted by ℰ R, is
a graph whose vertex set is the set of all nonzero proper ideals of R and two vertices I and J …

Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted
by Γ′(R), is a graph with vertices in W*(R), which is the set of all non-zero and non-unit …

Let R be a commutative ring with identity. Let G be a graph with vertices as elements of R,
where two distinct vertices a and b are adjacent if and only if there is a maximal ideal of R …

Let (Γ (R)) c be the maximal graph of a commutative ring with identity R whose vertices are
elements of R. Two distinct vertices a and b are adjacent if and only if Ra+ Rb≠ R or there …

Let R be a commutative ring and I its proper ideal, let S (I) be the set of all elements of R that
are not prime to I. Here we introduce and study the total graph of a commutative ring R with …

Let R be a commutative ring with identity. The prime ideal sum graph of R, denoted by PIS
(R), is a graph whose vertices are nonzero proper ideals of R and two distinct vertices I and …

For a commutative ring R with identity, the annihilating-ideal graph of R, denoted 𝔸𝔾 (R), is
the graph whose vertices are the nonzero annihilating ideals of R with two distinct vertices …