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.

Key Points

• The graph K4,7 is a complete bipartite graph, which means there are two sets of vertices, one set with 4 vertices and the other set with 7 vertices. Every vertex in one set is connected to every vertex in the other set.
• The radius (R) of a graph is defined as the minimum eccentricity of any vertex in the graph. The eccentricity of a vertex is the greatest distance from that vertex to any other vertex in the graph.
• The diameter (D) of a graph is the maximum eccentricity of any vertex in the graph. It represents the largest distance between any pair of vertices in the graph.
• In the case of the graph K4,7, the radius (R) is 2 and the diameter (D) is 2. This is because in a complete bipartite graph, any vertex in one set is at most 2 edges away from any vertex in the other set, and vice versa.
• Therefore, the ordered pair (R, D) for the graph K4,7 is (2, 2).

Additional Information

• The concepts of radius and diameter are fundamental in graph theory and are used to measure the "spread" of a graph.
• In a complete bipartite graph K_m,n, the radius and diameter are always 2 for m, n ≥ 1.
• These properties are useful in network design and analysis, where the efficiency of communication between nodes is important.
• Understanding these concepts helps in solving problems related to network routing, optimization, and connectivity.