Definition: A graph is called planar if can be drawn in one plane without any arcs crossing each other. Definintion: The graph G = (V,E) is called bipartite if the nodes can be divided into two disjunct parts V = V1∨ V2. where V1dosen’t have any elemenets in common with V2. Eulers polyhedronformula: Let G = (V, E) be a planar, connected graph and let v denote the number of nodes, e the number of arcs and r be the number of surfaces. Thenv – e + r = 2.Ex. For the dodecaedron, the number of surfaces is 12 similar pentagons. v = 20, e = 30 and r = 12.