What is an equivalence relation in graphs

Question

javk · Answer

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javk · Answer

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loser66 · Answer

Equivalence relation satisfies 3 conditions:
a) reflexive 
b) transitive 
c) symmetry
Hence R defined by $\omega_1R ~\omega_ 2$ =w1=w2 have the same length
a) reflexive: $\omega_1 ~R~\omega_1$ walk w1= itself . (Always, right?)$\surd$
b) transitive: $\omega_1~R~\omega_2$ and $\omega_2~R~\omega_3$, then $\omega_1~R~\omega_3$ , w1=w2, w2 =w3, then w1=w3 $\surd$
c) symmetry $\omega_1~~R~~\omega_2=\omega_2~~R~~\omega_1$, that is w1=w2, then w2=w1
Hence R is equivalence relation

loser66 · Answer

2) walk 123, that is you go from1 to2 then to 3, 
Now you find a way go to 3 with the same length . If you go directly from 1 to 3, but the length 1to 3 not equal the length 1to2 +2 to3, right?|dw:1430308481572:dw|