K5 Graph Properties and Non-Planarity

The video tutorial discusses the properties of the complete graph K5, which has 5 vertices and 10 edges. It explores whether K5 is planar by assuming it is and using Euler's formula to calculate R. The assumption leads to a contradiction, proving that K5 is non-planar. The tutorial uses a real-world analogy of 5 friends trying to connect their houses without intersecting roads to illustrate the concept of non-planarity.

What is the structure of a K5 graph?

• A bipartite graph with 5 vertices

• A complete graph with 5 vertices

• A tree with 5 vertices

• A cycle graph with 5 vertices

How many vertices does a K5 graph have?

• 5

• 4

• 3

• 6

What is the degree of each vertex in a K5 graph?

• 5

• 3

• 6

• 4

How many edges are there in a K5 graph?

• 20

• 15

• 10

• 5

What is the total degree of all vertices in a K5 graph?

• 10

• 15

• 20

• 25

What is the sum of the degrees of all vertices in a complete graph with n vertices?

• n^2 - n

• n^2

• n(n+1)

• n(n-1)

What is the formula used to check if a graph is planar?

• V - E + R = 2

• V + E + R = 2

• V + E - R = 2

• V - E - R = 2

What is the value of R when assuming K5 is planar?

• 6

• 8

• 7

• 5

What is the relationship between vertices (V), edges (E), and regions (R) in a planar graph?

• V - E + R = 4

• V - E + R = 2

• V - E + R = 1

• V - E + R = 3

What inequality must hold true for a graph to be planar?

• 3R > 2E

• 3R >= 2E

• 3R < 2E

• 3R = 2E