DM_11 - Discrete Mathematics(CSC 1204 9.4 Connectivity 9.5 Euler and Hamilton Paths 1 Paths A path is a sequence of edges that begins at a vertex of a

# DM_11 - Discrete Mathematics(CSC 1204 9.4 Connectivity 9.5...

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Discrete Mathematics (CSC 1204) 9.4 Connectivity 9.5 Euler and Hamilton Paths 1
Paths 2
Paths n . 3
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 connected if there is a path between every pair of distinct vertices of the graph 5
6 .
Example 5 (p.624) 7 Figure 2: The Graphs G 1 and G 2 The graph G l in Figure 2 is connected , because for every pair of distinct vertices there is a path between them. However, the graph G 2 in 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? Connectivity 1 2 3 4
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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 union 10
11 Connected Components Definition : A connected component in a graph G is 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? 6 2 4 3 5 1 7 8
Connected Components
Connectedness in Directed Graphs