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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 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 V1 and V2 such that every edge connects a vertex in V1 to a vertex in V2. V1 V2 V1 V2
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:
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.
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.
