lec09-graphs-rep - e 1 ·· e m The incidence matrix of G...

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EECS 203, Winter 2007 Discrete Mathematics Lecture 9 Graphs, continued February 1 Reading: Rosen [9.3] February 1 Graphs, continued, Page 1
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9.1 Adjacency lists An adjacency list of a graph G = ( V, E ) is a list of v V together with all the neighbors of v . Examples. Directed graph. February 1 Graphs, continued, Page 2
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9.2 Adjacency matrices Let G = ( V, E ) be a graph of n = | V | vertices. The adjacency matrix of G is a n × n matrix (or array, table, ...) A = [ a ij ] 1 i,j n such that a ij = 1 if and only if { i, j } ∈ E . Examples. February 1 Graphs, continued, Page 3
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9.3 Incidence matrices Let G = ( V, E ) be a graph of n = | V | vertices and m = | E | edges. Denote the edges by
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Unformatted text preview: { e 1 , ··· , e m } . The incidence matrix of G is a n × m matrix M = [ m i,j ] 1 ≤ i ≤ n, 1 ≤ j ≤ m ] so that m ij = 1 ⇐⇒ edge e j is incident to vertex i. Examples. February 1 Graphs, continued, Page 4 9.4 Graph Isomorphism Two graphs G 1 = ( V 1 , E 1 ) and G 2 = ( V 2 , E 2 ) are isomorphic if there is a one-to-one correspondence σ : V 1 → V 2 such that for any u, v ∈ V 1 , u 6 = v , { u, v } ∈ E 1 ⇐⇒ { σ ( u ) , σ ( v ) } ∈ E 2 . Examples. February 1 Graphs, continued, Page 5...
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