We consider a finite commutative ring with unity denoted by 𝒫. Within this framework, the essential graph of 𝒫 is represented as with Z(𝒫)* = Z(𝒫) \ {0} as the vertex set, and two distinct vertices x and y are adjacent if and only if ann (xy) is an essential ideal of 𝒫. At the same time, a weakly zero-divisor graph of 𝒫 is denoted by WΓ(𝒫) with Z(𝒫)* = Z(𝒫) \ {0} as the vertex set and an edge is defined between two distinct vertices u and υ if and only if there exist r ∈ ann(u)* and s ∈ ann(υ)* such that rs = 0, where ann(u) = {υ ∈ 𝒫: uυ = 0} for u ∈ 𝒫. In our research, we deal with the conditions under which both and WΓ(𝒫) can be classified as line graphs. Furthermore, we explore the scenarios in which these graphs are the complements of line graphs.
