An Information Upper Bound of Planar Graphs Using Triangulation

We propose a new linear time algorithm to represent a planar graph. Based on a specific triangulation of the graph, our coding takes on average 5.03 bits per node, and 3.37 bits per node if the graph is maximal. We derive from this representation that the number of unlabeled planar graphs with n nodes is at most 2 n+O(log n) , where 5.007. The current lowe