We consider graphs obtained by placing n points at random on a unit sphere in R, and connecting two points by an edge if they are close to each other (e.g., the angle at the origin that their corresponding unit vectors make is at most π/3). We refer to these graphs as geometric graphs. We also consider a complement family of graphs in which two points are connected by an edge if they are far aw...

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. Fur...