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Discrete Mathematics and its Applications (8th Edition)

10 Graphs

10.4 Connectivity

10.4.3 Connectedness in Undirected Graphs

Connected Component

Exercise: Prove that for any simple graph $G$, $G$ is connected or $\overline{G}$ is connected.

10.4.4 How Connected is a Graph?

• Cut Vertex
• Cut Edge / Bridge

$$\kappa (G)⩽\lambda (G)⩽\underset{v\in V}{\min }\mathrm{deg}(v)$$

10.4.5 Connectedness in Directed Graphs

• Strongly connected
• Weakly connected
• Strongly connected component

10.4.6 Paths and Isomorphism

10.5 Euler and Hamilton Paths

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See also

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