1. ساختمانهای گسسته دانشگاه صنعتی شاهرود – فروردین 1392

2. bipartite graph: (V,E) a graph whose vertex set V can be partitioned in two disjoint, nonempty sets V 1 and V 2 such that every edge connects a vertex in V 1 to a vertex in V 2. V1V1 V2V2 V1V1 V2V2 2

3. 3 Trees A tree is a connected graph which contains no cycles. Properties of Tree Every tree with n vertices has exactly n  1 edges. Any two vertices in a tree are connected by exactly one path.

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5. Examples for Isomorphic Graphs

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7. 10 7 Planar Graphs and Graph Coloring  A graph is a planar graph if and only if it has a pictorial representation in a plane which is a plane graph. This pictorial representation of a planar graph G as a plane graph is called a planar representation of G.  Let G denote the plane graph in Figure 10.111. Graph G, in Figure 10.111, divides the plane into different regions, called the faces of G.

8. 10 8 Planar Graphs and Graph Coloring

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10. Planar Graphs and Graph Coloring