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

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SUMMARY

The discussion centers on the concept of graph isomorphism and its implications for edge graphs. It is established that two graphs can be isomorphic, meaning they have the same structure despite potentially differing representations. The participants conclude that if a graph contains an isomorphic sub-graph, it cannot be classified as an edge graph. The necessity of labeling vertices and edges is emphasized for determining graph equality.

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  • Graph theory fundamentals
  • Understanding of graph isomorphism
  • Knowledge of edge graphs
  • Familiarity with vertex and edge labeling
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  • Study the properties of isomorphic graphs
  • Learn about edge graph definitions and characteristics
  • Explore techniques for labeling vertices and edges in graphs
  • Investigate practical applications of graph isomorphism in computer science
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Mathematicians, computer scientists, and students studying graph theory or working with graph algorithms will benefit from this discussion.

Cuttlas
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Hi

Are these two graphs EQUAL to each other?

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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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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?
 

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