If R and D are the radius and diameter of the graph K_4,7' then the ordered pair (R, D) is equal to :

The correct answer is: option 1: (2, 2)

Concept:

We are given the graph K_4,7, which is a complete bipartite graph with partitions of sizes 4 and 7. This means:

• There are two sets of vertices: Set A with 4 vertices and Set B with 7 vertices.
• Each vertex in Set A is connected to every vertex in Set B, and no vertex is connected within its own set.

Definitions:

• Radius (R): The minimum eccentricity of all vertices.
• Diameter (D): The maximum eccentricity of any vertex.
• Eccentricity: The greatest distance from a vertex to any other vertex.

In K_m,n (m ≥ 1 and n ≥ 1, and m,n ≥ 2):

• Every vertex in one partite set is connected directly to all vertices in the other set.
• Therefore, any two vertices from different sets are at distance 1.
• Any two vertices from the same set are at distance 2 (because they must go through a vertex in the other set).

So:

• Max eccentricity = 2 → Diameter D = 2
• Min eccentricity = 2 → Radius R = 2

Hence, the ordered pair (R, D) is: (2, 2)

Final Answer: option 1: (2, 2)