Line graph of unit graphs associated with finite commutative rings

For a given graph G, its line denoted by L(G) is whose vertex set V (L(G)) = E(G) and {e1, e2} ∈ E(L(G)) if e1 e2 are incident to common in G. Let R be finite commutative ring with nonzero identity G(R) denotes the unit associated R. In this manuscript, we have studied L(G(R)) of course investigation, several basic properties, viz., diameter, girth, clique, chromatic number been determined. Further, derived sufficient conditions for Planar Hamiltonian