What is the smallest number of edges in a non planar graph?

A plane graph having ‘n’ vertices, cannot have more than ‘2*n-4’ number of edges. Hence using the logic we can derive that for 6 vertices, 8 edges is required to make it a plane graph. So adding one edge to the graph will make it a non planar graph. So, 6 vertices and 9 edges is the correct answer.

What is minimal non planar graph?

A minimal nonplanar graph is a nonplanar graph that does not have any nonplanar proper subgraph. Clearly, it suffices to prove the statement for all G some minimal nonplanar graph.

Is a graph with no edges planar?

When a connected graph can be drawn without any edges crossing, it is called planar . When a planar graph is drawn in this way, it divides the plane into regions called faces . Draw, if possible, two different planar graphs with the same number of vertices, edges, and faces.

Which of the following is not a planar graph?

Which one of the following graphs is NOT planar? Explanation: A graph is planar if it can be redrawn in a plane without any crossing edges. G1 is a typical example of nonplanar graphs.

Is Petersen graph a planar graph?

Because it is nonplanar, it has at least one crossing in any drawing, and if a crossing edge is removed from any drawing it remains nonplanar and has another crossing; therefore, its crossing number is exactly 2. Each edge in this drawing is crossed at most once, so the Petersen graph is 1-planar.

What’s the maximum number of edges in a directed graph with n vertices?

In a directed graph having N vertices, each vertex can connect to N-1 other vertices in the graph(Assuming, no self loop). Hence, the total number of edges can be are N(N-1).

What are the number of edges of K3 3?

9 edges
K5 has 10 edges and 5 vertices while K3,3 has 9 edges and 6 vertices.

Is K3 3 a planar?

The graph K3,3 is non-planar.

What is a non planar graph Mcq?

Explanation: A non-planar graph can have removed edges and vertices so that it contains subgraphs. However, non-planar graphs cannot be drawn in a plane and so no edge of the graph can cross it.

Is QK planar?

Yes- it’s a planar graph(sorry) and Qn is hypercube with n vertices. Related question.