# DS09_Ch09a - CHAPTER 9 GRAPH ALGORITHMS 1 Definitions G V E...

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CHAPTER 9 GRAPH ALGORITHMS §1 Definitions G( V, E ) where G ::= graph, V = V( G ) ::= finite nonempty set of vertices, and E = E( G ) ::= finite set of edges. Undirected graph: ( v i , v j ) = ( v j , v i ) ::= the same edge. Directed graph (digraph): < v i , v j > ::= < v j , v i > v i v j tail head Restrictions : (1) Self loop is illegal. (2) Multigraph is not considered 0 1 0 1 2 Complete graph: a graph that has the maximum number of edges 0 2 1 3 2 ) 1 ( 2 E of # V of # - = = = n n n C n 0 2 1 3 ) 1 ( E of # V of # 2 - = = = n n P n n 1/7

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v i v j v i and v j are adjacent ; ( v i , v j ) is incident on v i and v j v i v j v i is adjacent to v j ; v j is adjacent from v i ; < v i , v j > is incident on v i and v j Subgraph G’ G ::= V( G’ ) V( G ) && E( G’ ) E( G ) Path ( G) from v p to v q ::= { v p , v i 1 , v i 2 , ⋅ ⋅ ⋅ , v in , v q } such that ( v p , v i 1 ), ( v i 1 , v i 2 ), ⋅ ⋅ ⋅ , ( v in , v q ) or < v p , v i 1 >, ⋅ ⋅ ⋅ , < v in , v q > belong to E( G ) Length of a path ::= number of edges on the path Simple path
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DS09_Ch09a - CHAPTER 9 GRAPH ALGORITHMS 1 Definitions G V E...

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