Understanding Connected Planar Graphs

The video tutorial explores whether a graph with eight vertices and edges can be a connected planar graph. It introduces the concept of connected planar graphs and explains Euler's formula, which is used to determine if a graph is planar. The formula is applied to a graph with eight vertices and edges, showing that it can be a connected planar graph if it has two faces. The tutorial concludes with an example of such a graph, specifically the cycle on eight vertices (C8), which satisfies the conditions of being connected and planar.

What is a connected planar graph?

• A graph with no vertices.

• A graph where all vertices are connected and edges do not cross.

• A graph with only one vertex.

• A graph with edges that cross each other.

What is the purpose of Euler's formula in planar graphs?

• To calculate the number of vertices.

• To count the number of edges.

• To find the shortest path in a graph.

• To determine if a graph is connected and planar.

What is Euler's formula for planar graphs?

• V + E = F

• V / E = F

• V - E + F = 2

• V * E = F

How many vertices and edges does the graph in the problem have?

• Eight vertices and eight edges.

• Ten vertices and eight edges.

• Eight vertices and ten edges.

• Ten vertices and ten edges.

What is the unknown variable in Euler's formula for this problem?

• The number of vertices (V).

• The number of edges (E).

• The number of faces (F).

• The number of loops.

What conclusion is reached after applying Euler's formula?

• The graph is planar with two faces.

• The graph cannot be planar.

• The graph has more than eight vertices.

• The graph has no edges.

What is the cycle on eight vertices referred to in the video?

• A graph with eight vertices and edges forming a cycle.

• A graph with eight disconnected vertices.

• A graph with eight vertices and no edges.

• A graph with eight vertices and multiple loops.

How many faces does the C8 graph have?

• One face.

• Four faces.

• Two faces.

• Three faces.