Discrete Mathematics(CSC 1204) 9.4 Connectivity9.5 Euler and Hamilton Paths1
Paths in Directed Graph•Same as in undirected graphs, but the path must go in the direction of the arrows.4
Connectedness in Undirected Graphs•An undirected graph is called connectedif there is a path between every pair of distinct vertices of the graph5
Example 5 (p.624)7Figure 2: The Graphs G1and G2The graph Glin Figure 2 is connected, because for every pair of distinct vertices there is a path between them. However, the graph G2in Figure 2 is not connected. For instance, there is no path in G2 between vertices a and d.
8•Question: Which of the following graphs are connected?Connectivity1234
Connected Components•A connected component of a graph G is a connected subgraph of G that is not proper subgraph of another connected subgraph of G.•A connected component of a graph G is a maximal connected subgraph of G.–A graph G that is not connected has two or more connected components that are disjoint and have G as their union10
11Connected Components•Definition: A connected component in a graph Gis a set of vertices such that all vertices in the set are connected to each other and every possible connected vertex is included.•Question: What are the connected components of the following graph?62435178