Can a graph be an edge graph if it contains an isomorphic sub-graph?

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In summary, the concept of equality between two graphs is not very useful as it depends on labeling the vertices and edges. However, the graphs in question are isomorphic, meaning they have the same structure. Therefore, if a graph contains the right graph as a sub-graph, it cannot be an edge graph because it is the same as the left graph.
  • #1
Cuttlas
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Hi

Are these two graphs EQUAL to each other?

87zw63kfl1067h17g.jpg


Exactly If a Graph contains the left graph in image as a sub-graph then it can not be an edge graph. the question is about the right one, Is it equal with left one? if yes, then does it mean If a Graph contains the right graph in image as a sub-graph too then it can not be an edge graph because it is the same as left one?

Please help me solve this small problem :)
 
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  • #2
You have not given sufficient information to determine equality. Indeed, you must label the vertices and the edges, and only then can we decide equality.

But to be honest, equality of graphs is not a very useful concept. What is certainly true is that the graphs in question are isomorphic. And because of this, the answer to your following question is yes:

does it mean If a Graph contains the right graph in image as a sub-graph too then it can not be an edge graph because it is the same as left one?
 

1. What is the significance of the equality of two graphs?

The equality of two graphs indicates that they have the same shape, location, and distribution of data points. This means that the two variables being compared have the same relationship and can be used interchangeably.

2. How can you tell if two graphs are equal?

To determine equality between two graphs, you can visually compare their shapes and data points. Additionally, you can perform statistical tests such as correlation analysis or hypothesis testing to determine if there is a significant difference between the two graphs.

3. What factors can affect the equality of two graphs?

The equality of two graphs can be affected by various factors such as sample size, data collection methods, and the type of data being compared. It is important to consider these factors when determining the equality of two graphs.

4. Can two graphs be equal but not identical?

Yes, two graphs can be equal but not identical. This means that they may have the same shape and data points, but they may differ in other characteristics such as scale or labels. It is important to carefully compare the two graphs to determine their equality.

5. What are the limitations of using graph equality to make conclusions?

While graph equality can provide valuable insights, it is important to note that it does not necessarily imply causation or a strong relationship between the two variables. Other factors may also need to be considered before making conclusions based on graph equality alone.

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