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physix123
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how would you go about showing that a subgroup and dihedral group- of the same order- are not isomorphic?
"Prove not isomorphic" is a statement that is used in graph theory to indicate that two given graphs are not isomorphic, meaning that they cannot be rearranged or redrawn to look exactly the same. It is a way of proving that two graphs are structurally different.
In order to prove that two graphs are not isomorphic, you need to demonstrate that they have different properties or characteristics, such as different numbers of vertices, edges, or cycles. You can also look at the degree sequence, connectivity, or other structural properties to show that the graphs are not isomorphic.
Yes, it is possible for two graphs to have the same number of vertices and edges, but not be isomorphic. This is because isomorphism is not just about the number of vertices and edges, but also about the overall structure and connectivity of the graphs.
Proving not isomorphic is important in graph theory because it helps to identify and distinguish between different types of graphs. It also allows us to better understand the properties and relationships between graphs, which can have applications in fields such as computer science and chemistry.
There are some common properties that can be quickly checked to determine if two graphs are not isomorphic, such as the number of vertices, edges, and degree sequence. However, there is no universal shortcut or trick for proving not isomorphic, as it ultimately depends on the specific characteristics and properties of the graphs in question.