Bar 1-visibility representation of optimal 1-planar graph

In a visibility representation of a graph, the vertices map to objects in Euclidean space and the edges are determined by certain visibility relations. A bar visibility representation of a planar graph is a drawing where each vertex is drawn as a horizontal line segments called bars, each edge is drawn as a vertical line segment where the vertical line segment representing an edge must connect the horizontal line segments representing the end vertices. A graph is called a 1-planar graph if it can be drawn in the plane so that each its edge is crossed by at most one other edge. A 1-planar graph is said to be optimal if there are highest number of edges available. In this Research, we proposed an algorithm to numbering the optimal 1-planar graph and also bar 1-visibility representation of optimal 1-planar graph.