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Chapter 4 Graphs

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**4.1 GRAPHS AND THEIR REPRESENTATIONS**

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**Other Representations of Graphs**

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Isomorphism

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4.2 PATHS AND CIRCUITS A multigraph consists of a nonempty finite set of vertices and a set of edges, where we allow an edge to join a vertex to itself or to a different vertex, and where we allow several edges joining the same pair of vertices. An edge from a vertex to itself is called a loop. When there is more than one edge between two vertices, these edges are called parallel edges.

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**Euler Circuits and Paths**

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**4.3 SHORTEST PATHS AND DISTANCE**

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Weighted Graphs

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4.4 COLORING A GRAPH

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**4.5 DIRECTED GRAPHS AND MULTIGRAPHS**

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**Representations of Directed Graphs**

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**Directed Euler Circuits and Paths**

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**Directed Hamiltonian Cycles and Paths**

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