Final answer:
In order to find an example of a small graph G = (V, E) and an originator u such that b (u, G) < dist. (u, C) + bmin(G), you need to understand the concepts of b (u, G), dist. (u, C), and bmin(G). For example, let's consider a small graph G = (V, E) with 4 vertices: V = {A, B, C, D} and 4 edges: E = {(A, B), (B, C), (C, D), (D, A)}. Let u be the originator vertex. In this case, b (u, G) = 0, dist. (u, C) = 2, and bmin(G) = 0. Therefore, b (u, G) < dist. (u, C) + bmin(G) holds true.
Step-by-step explanation:
In order to find an example of a small graph G = (V, E) and an originator u such that b (u, G) < dist. (u, C) + bmin(G), we need to understand the concepts of b (u, G), dust (u, C), and bmin(G).
b (u, G) represents the number of vertices that originate from vertex u in graph G. dist. (u, C) represents the shortest path between vertex u and vertex C in graph G. bmin(G) represents the minimum number of originators in any graph G.
For example, let's consider a small graph G = (V, E) with 4 vertices: V = {A, B, C, D} and 4 edges: E = {(A, B), (B, C), (C, D), (D, A)}. Let u be the originator vertex. In this case, b (u, G) = 0, dist. (u, C) = 2, and bmin(G) = 0. Therefore, b (u, G) < dist. (u, C) + bmin(G) holds true.
An infinite class of graphs that satisfies this condition can be obtained by adding more vertices and edges to the initial graph G while maintaining the same originator u. As long as there is no direct connection between the originator vertex u and vertex C, the condition b (u, G) < dist. (u, C) + bmin(G) will continue to hold true.