discrete math

[matt271]

there is no math section so i didnt know where to post this.

anywaysssssss i am just wondering if anybody can explain how to show two graphs are isomorphic?

i dont have the text book. but i did google it and i found this Wikipedia page http://en.wikipedia.org/wiki/Graph_isomorphism
i did it exactly like this example, but on my midterm the teacher took away points.

i went to ask why he took away points but there is a language barrier with this teacher.
all i gathered is that he wanted me to define some function like "f : a -> b" but i have never seen this format before.

my exam is tomorrow just wondering if anybody can explain it real quick??

this is a different question then was on my midterm but i think its more interesting because there's no graph:

Let T = {x|x divides 3} show that (T, +) and (Z, +) are isomorphic.


can i just say f(n) = 3n , n belongs to Z ?

ty

[saltpro15]

you can put it in off-topic, and I just finished gr10 math, so no idea, sorry

[matt271]

saltpro15 @ Wed Apr 08, 2009 8:55 pm wrote:

you can put it in off-topic, and I just finished gr10 math, so no idea, sorry

got me all excited for nothing

haha

[Tony]

matt271 @ Wed Apr 08, 2009 7:35 pm wrote:

he wanted me to define some function like "f : a -> b" but i have never seen this format before.

It's a one-to-one (injective) function. If you also define "f2 : b -> a" (onto (surjective)) then f and f2 create a bijection, which shows isomorphism of a and b.

[matt271]

k i got it ty ty

[Brightguy]

Tony @ Wed Apr 08, 2009 8:20 pm wrote:

It's a one-to-one (injective) function. If you also define "f2 : b -> a" (onto (surjective)) then f and f2 create a bijection, which shows isomorphism of a and b.

This shows |a| <= |b|. A bijection is a single function (one that is injective and surjective).

matt271 @ Wed Apr 08, 2009 7:35 pm wrote:

Let T = {x|x divides 3} show that (T, +) and (Z, +) are isomorphic.

Well, you mean T = { x | 3 divides x }. You have to give a bijective function f: Z -> T which preserves the addition structure, i.e., f(a+b)=f(a)+f(b). You've found f, you just have to show it satisfies the necessary properties. One way to show f is bijective is to give its inverse.

LaTeX is broken again? You guys are killing me.