tailieunhanh - Chapter 9 - Graph•

A Graph G consists of a set V, whose members are called the vertices of G, together with a set E of pairs of distinct vertices from V. • The pairs in E are called the edges of G. • If the pairs are unordered, G is called an undirected graph or a graph. Otherwise, G is called a directed graph or a digraph. • Two vertices in an undirected graph are called adjacent if there is an edge from the first to the second. | Chapter 9 - Graph A Graph G consists of a set V whose members are called the vertices of G together with a set E of pairs of distinct vertices from V. The pairs in E are called the edges of G. If the pairs are unordered G is called an undirected graph or a graph. Otherwise G is called a directed graph or a digraph. Two vertices in an undirected graph are called adjacent if there is an edge from the first to the second. 1 Chapter 9 - Graph A path is a sequence of distinct vertices each adjacent to the next. A cycle is a path containing at least three vertices such that the last vertex on the path is adjacent to the first. A graph is called connected if there is a path from any vertex to any other vertex. A free tree is defined as a connected undirected graph with no cycles. 2 Chapter 9 - Graph In a directed graph a path or a cycle means always moving in the direction indicated by the arrows. A directed graph is called strongly connected if there is a directed path from any vertex to any other vertex. If we suppress the direction of the edges and the resulting undirected graph is connected we call the directed graph weakly connected