91Ó°ÊÓ

Use a graph to model the tournament. The teams are the vertices. Describe the kind of graph used. There is an edge between teams if the teams played.

Use a graph to model the tournament. The teams are the vertices. Describe the kind of graph used. There is an edge from team \(t_{i}\) to team \(t_{j}\) if \(t_{i}\) beat \(t_{j}\) at least one time.

Use a graph to model the tournament. The teams are the vertices. Describe the kind of graph used. There is an edge between teams for each game played.

Use a graph to model the tournament. The teams are the vertices. Describe the kind of graph used. There is an edge from team \(t_{i}\) to team \(t_{j}\) for each victory of \(t\) over \(t_{j}\).

Write the adjacency matrix of each graph. The complete bipartite graph \(K_{2,3}\)

Write an algorithm that finds the length of a shortest path between two given vertices in a connected, weighted graph and also finds a shortest path.

Tell whether the given path in the graph is (a) A simple path (b) A cycle (c) A simple cycle (b, c, d, a, b, e, d, c, b)

Write the adjacency matrix of each graph. The complete graph on five vertices \(K_{5}\)

Write an algorithm that finds the lengths of the shortest paths from a given vertex to every other vertex in a connected, weighted graph \(G\).

Write an algorithm that finds the lengths of the shortest paths between all vertex pairs in a simple, connected, weighted graph having \(n\) vertices in time \(O\left(n^{3}\right)\).