Chapter 4 Graphs

4.1 GRAPHS AND THEIR REPRESENTATIONS

Other Representations of Graphs

Isomorphism

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.

Euler Circuits and Paths

4.3 SHORTEST PATHS AND DISTANCE

Weighted Graphs

4.4 COLORING A GRAPH

4.5 DIRECTED GRAPHS AND MULTIGRAPHS

Representations of Directed Graphs

Directed Euler Circuits and Paths

Directed Hamiltonian Cycles and Paths