A Note on Full and Complete Binary Planar Graphs

Abstract

Let G=(V(G), E(G)) be a connected graph where V(G) is a finite nonempty set called vertex-set of G, and  E(G) is a set of unordered pairs {u, v} of distinct elements from  V(G) called the edge-set of G. If  is a connected acyclic graph or a connected graph with no cycles, then it is called a tree graph. A binary tree Tl with l levels is complete if all levels except possibly the last are completely full, and the last level has all its nodes to the left side. If we form a path on each level of a full and complete binary tree, then the graph is now called full and complete binary planar graph and it is denoted as Bn, where n is the level of the graph. This paper introduced a new planar graph which is derived from binary tree graphs. In addition, a combinatorial formula for counting its vertices, faces, and edges that depends on the level of the graph was developed.