lec08-graphs

# lec08-graphs - EECS 203 Winter 2007 Discrete Mathematics...

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EECS 203, Winter 2007 Discrete Mathematics Lecture 8 Graphs January 30 Reading: Rosen [9.1-9.2] January 30 Graphs, Page 1

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8.1 Graphs Informally: a set of dots connected by lines. Examples of graphs Social graphs. Co-authorship graphs. A simple graph G = ( V, E ) consists of a finite set V of vertices , and a set of edges E ⊆ {{ u, v } : u, v V, u = v } . If an edge e = { u, v } , u and v are called the endpoints of e , and e is said to be incident to u and v , and e connects u and v , and u and v are adjacent , and u is a neighbor of v . The degree of a vertex is the number of its neighbors. January 30 Graphs, Page 2
8.1 Graphs Special graphs Complete graphs Empty graphs Path, cycles Hypercube Peterson graph Johnson graph (Kneser graph) Bipartite graph: a simple graph G = ( V, E ) is bipartite if there is a partition of V into two disjoint sets V 1 and V 2 such that E ⊆ {{ u, v } : u V 1 , v V 2 } . Regular graph: a graph is regular if the degree of every vertex is the same.

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