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The Petersen graph is a graph with 10 vertices and 15 edges. enter image description here

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

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


1 Answer

Yes, we can.${}{}{}{}{}{}{}{}$

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can we say any graph with 10 vertices and 15 edges is Petersen graph? –  kalpeshmpopat Mar 14 '13 at 10:19
@kalpeshmpopat No. It seems you are misunderstanding something here. If you tell us exactly what your definition of a graph is, and what your definition of two graphs being isomorphic is (and start being a little more polite to people who are using their free time to help you), then somebody here can probably help you overcome this misunderstanding. –  Matt Pressland Mar 14 '13 at 10:25
@kalpeshmpopat This question makes more sense, but the answer is no. Look at the graph above, remove an edge which connects two "outer" vertices and add an edge between two "inner" vertices. Those graphs are not isomorphic, because the new graph has vertices with degree 4. –  Laugerizor Mar 14 '13 at 10:27
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
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