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Graph Theory

Graph Theory . هواللطیف. ساختمانهای گسسته دانشگاه صنعتی شاهرود – فروردین 1392. bipartite graph: (V,E) an undirected 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 . V 1. V 2.

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Graph Theory

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  1. Graph Theory هواللطیف ساختمانهای گسسته دانشگاه صنعتی شاهرود – فروردین 1392

  2. bipartite graph: (V,E) an undirected graph whose vertex set V can be partitioned in two disjoint, nonempty sets V1 and V2 such that every edge connects a vertex in V1 to a vertex in V2. V1 V2 V1 V2

  3. B C E A D people v jobs z u x y Other Graph Problems: AssignmentProblem • Given: n people and n jobs Each person can be assigned to exactly one job Each job should be assigned to exactly one person Person-job compatibility is given by a directed graph (e.g., having a link A  x means “person A can do job x ”) • Goal: Find an assignment of n jobs to n people (if such an assignment exists). • Example:

  4. 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.

  5. Examples for Isomorphic Graphs

  6. 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.

  7. Planar Graphs and Graph Coloring

  8. Planar Graphs and Graph Coloring

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