12. Graph and Their Applications

12. Graph and Their Applications - Graph and Its...

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Graph and Its Applications 1
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Graph Nonlinear data Structures. A graph G consists of two properties: (a) A set V of elements called vertices or nodes. (b) A set E of connectors called edges such that each edge e is identified as e = [u,v] (unordered pair of vertices). Here u and v are called endpoints of e and they are said to be the adjacent nodes or neighbors . Example: A B C D E In Graph G 1 5 Vertices:{A, B, C, D, E} 6 Edges: {[A,B], [A,C], [B,D], [B,E], [C,D], [D,E]} Figure1: A graph G 1 Graph and Their Applications Graph and Their Applications 2
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Definitions Isolated Node: A vertex u with no edges. Path: A path P of length n from a node u to node v is defined as a sequence n+1 nodes such that P=(v 0 , v 1 , ….v n ). (a) Simple Path: if all nodes in path P are distinct. (b) Closed Path: If node v 0 = v n . Cycle: A closed path, with no other repeated vertices other than the starting and the ending vertices. Example: A B C D E In graph G 2 Isolate Node: E Path P: A, B, D, C • Cycle C 1 : A, B, D, C, A Figure2: Graph G 2 3
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