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# path simplepath sequenceofalternating

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Unformatted text preview: 5 Terminology (cont.) Path Simple path sequence of alternating vertices and edges begins with a vertex ends with a vertex each edge is preceded and followed by its endpoints path such that all its vertices and edges are distinct Examples P1=(V,b,X,h,Z) is a simple path P2=(U,c,W,e,X,g,Y,f,W,d,V) is a path that is not simple © 2010 Goodrich, Tamassia Graphs a U c V b d P2 e W f P1 X h Z g Y 6 Terminology (cont.) Cycle Simple cycle circular sequence of alternating vertices and edges each edge is preceded and followed by its endpoints cycle such that all its vertices and edges are distinct Examples C1=(V,b,X,g,Y,f,W,c,U,a,↵ ) is a simple cycle C2=(U,c,W,e,X,g,Y,f,W,d,V,a,↵ ) is a cycle that is not simple © 2010 Goodrich, Tamassia Graphs a U c V b d C2 X e W f h Z C1 g Y 7 Properties Property 1 Notation Σ v deg(v) = n m deg(v) 2m Proof: each edge is counted twice Property 2 Example n= 4 m= 6 deg(v) =3 In an undirected graph with no self­loops and no multiple edges m ≤ n (n − 1)/ 2 Proof: each vertex...
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