# The Petersen Graph and its isomorphisms [closed]

The Petersen graph is a graph with 10 vertices and 15 edges.

Can we find a graph that is isomorphic to Petersen graph?

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## closed as not a real question by Alexander Gruber♦, Stefan Hansen, draks ..., Dennis Gulko, MicahMar 14 '13 at 12:23

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

Do you even have any idea what the words you're saying mean? –  Alexander Gruber Mar 14 '13 at 9:16
Find a graph which is isomorphic to Petersen graph –  kalpeshmpopat Mar 14 '13 at 9:18
Here's one. –  Alexander Gruber Mar 14 '13 at 9:19
Every graph is isomorphic to itself, and so the answer to this question is rather trivial (as evidenced by Alexander Gruber's comment above). Either you mis-understand the concept of isomorphic, or you are not asking the question to actually mean to ask. –  Arthur Fischer Mar 14 '13 at 9:21
@kalpeshmpopat Matt Pressland knows the answer because it's a very, very easy question. Don't ask questions about whether graphs are isomorphic if you haven't looked up the definition of isomorphic. This isn't Google. –  Alexander Gruber Mar 14 '13 at 9:39

Yes, we can.${}{}{}{}{}{}{}{}$
Look, any question of the type "Can we find a structure that is isomorphic to [some given structure]" will have the affirmative answer I gave. It becomes potentially more interesting if one asks "not isomorphic" instead of "isomorphic", with maybe some additional restrictions. However even if you ask: "can we find a graph with $10$ vertices all of degree $3$ that is not isomorphic to the Petersen graph", then the answer is still affirmative (select an edge, then a pair of neigbouring edges, and switch their other endpoints). –  Marc van Leeuwen Mar 14 '13 at 11:29