Graphs 1.2 - Paths Path sequence of alternating vertices...

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Unformatted text preview: Paths Path sequence of alternating vertices and edges begins with a vertex ends with a vertex V a each edge is preceded and followed by its endpoints Simple path P1 d U c path such that all its vertices and edges are distinct Examples b X P2 h Z e W g f P1=(V,b,X,h,Z) is a simple path Y P2=(U,c,W,e,X,g,Y,f,W,d,V) is a path that is not simple CSE 2011 Prof. J. Elder -6- Last Updated: 4/1/10 10:16 AM Cycles Cycle circular sequence of alternating vertices and edges each edge is preceded and followed by its endpoints a Simple cycle cycle such that all its vertices and edges are distinct U b d X C2 e c Examples C2=(U,c,W,e,X,g,Y,f,W,d,V,a, ) is a cycle that is not simple -7- h Z C1 W C1=(V,b,X,g,Y,f,W,c,U,a, ) is a simple cycle CSE 2011 Prof. J. Elder V g f Y Last Updated: 4/1/10 10:16 AM Subgraphs A subgraph S of a graph G is a graph such that The vertices of S are a subset of the vertices of G Subgraph The edges of S are a subset of the edges of G A spanning subgraph of G is a subgraph that contains all the vertices of G Spanning subgraph CSE 2011 Prof. J. Elder -8- Last Updated: 4/1/10 10:16 AM Connectivity A graph is connected if there is a path between every pair of vertices A connected component of a graph G is a maximal connected subgraph of G Connected graph Non connected graph with two connected components CSE 2011 Prof. J. Elder -9- Last Updated: 4/1/10 10:16 AM Trees Tree Forest Graph with Cycle A tree is a connected, acyclic, undirected graph. A forest is a set of trees (not necessarily connected) CSE 2011 Prof. J. Elder - 10 - Last Updated: 4/1/10 10:16 AM ...
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