Answer to Question #129760 in Discrete Mathematics for Gazal

Question

S.T if G is a polyhedral graph then there is a region of degree ≤ 5

Answer 1

A graph is polyhedral if it is the graph formed by the vertices and edges of convex polyhedron.

Graph formed by vertices and edges of convex polyhedron. A graph is k-vertex connected, if one vertex is remove then resulting graph disturb or disconnected and its having 3 degree of freedom motion abut its 3 vertices and 1 degree of freedom is normal to plane hence polyhedral graph maximum 4 degree ,hence if G is a polyhedral graph then there is a region of degree ≤ 5.

after redraw ,