planar graph

In an undirected connected planar graph G, there are eight vertices and five faces. The number of edges in G is ______

The minimum number of colours that is sufficient to vertex-colour any planar graph is _____________ .

Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is ___________.

Let $$\delta $$ denote the minimum degree of a vertex in a graph. For all planar graphs on $$n$$ vertices with $$\delta \ge 3$$, which one of the following is TRUE?

The line graph $$L(G)$$ of a simple graph $$G$$ is defined as follows: $$\,\,\,\,$$There is exactly one vertex $$v(e)$$ in $$L$$(G)$$ for each edge $$e$$ in $$G$$ $$\,\,\,\,$$ For...

Let G be a simple undirected planner graph on 10 vertices with 15 edges. If G is a connected graph, then the number of bounded faces in any embedding of G on the plane is equal to

Let $$G$$ be a simple connected planar graph with 13 vertices and 19 edges. Then, the number of faces in the planar embedding of the graph is:

Maximum number of edges in a planar graph with $$n$$ vertices is _______ .

A graph is planar if and only if,