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up vote 0 down vote favorite I have a beginner Graph theory question. We just started learning it for my discrete math class and I'm confused about the wording of this question. In the examples done in class and in the textbook, the set of vertices is always represented as a single set of finite integers. In this question however, it says the vertices are the sets {a,b}. Could someone clarify what exactly this means and the implications of this, as well as any hints for the question? Thanks a lot graph-theory share | cite | improve this question asked Nov 15 at 23:41 tkon 16 1 ...

up vote 1 down vote favorite 1 I have a question: it is true that if $H_1$ and $H_2$ are cyclic groups that are isomorphic, then $G/H_1$ is isomorphic to $G/H_2$ ? I know that if I remove the condition "cyclic groups", the given statement is false and there are numerous counterexamples that disproves it, but I don't know if my statement is true and I don't how to create a counterexample or to prove it. If it is true, can you give me a hint about how can this be proven? For example, I just have shown that $Z_{12}/ langle 2 rangle$ is isomorphic to $Z_{12}/Z_6$ which is isomorphic to $Z_3$ (since both $langle 2 rangle$ and $Z_6$ are isomorphic). How this can be generalized? group-theory normal-subgroups ...