if and only if 1 − ab is not a unit of R. Also,

the line graph of the Jacobson graph is denoted by L(JR). In this paper, we characterize all finite

commutative rings R such that the graphs L(JR) are planar, toroidal or projective....

In this paper, we investigate when the unit, unitary and total graphs have

planar line graph, and also we study the case when these line graphs are ring graph or

outerplanar....

. In this paper we characterize the finite Jacobson graphs which are chordal graphs, cographs, line graphs, or interval graphs. Among other results, we find the degree set of finite Jacobson graphs, and the number of vertices with specific degree....

A connected graph G is said to be neighbourly irregular graph if no two

adjacent vertices of G have same degree. In this paper we obtain neighbourly irregular

subdivision graphs, line graphs and total graphs. The neighbourly...

Let R be a commutative ring with nonzero identity and G be

a nontrivial finite group. Also, let Z(R) be the set of zero-divisors of R

and, for a ∈ Z(R), let ann(a) = {r ∈ R | ra = 0}. The annihilator ...