Construct all possible non-isomorphic graphs on four vertices with at most 4 edges.
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I'm new to graph theory and I don't plan to become a serious student of graph theory either. My book suggests that there are 1111non-isomorphic graphs of order 44, but I can't see why.
I know that the most naive approach is that I can use brute force and draw four vertices and then try to connect two vertices by an edge in such a way that I don't get isomorphic graphs in each step. But then the question is, how should I know I have counted all possibilities at the end? And when the size of the graph becomes larger, how should I know I'm not counting two isomorphic structures more than once?
To be more precise, I have 5 questions about determining the number of non-isomorphic graphs with nn vertices:
I know that the most naive approach is that I can use brute force and draw four vertices and then try to connect two vertices by an edge in such a way that I don't get isomorphic graphs in each step. But then the question is, how should I know I have counted all possibilities at the end? And when the size of the graph becomes larger, how should I know I'm not counting two isomorphic structures more than once?
To be more precise, I have 5 questions about determining the number of non-isomorphic graphs with nn vertices:
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