I Circuits or edge-disjoint unions of circuits in a connected graph

cianfa72 · Jun 7, 2023

Hi,
I've a question related to the graph theory.

Take a connected graph with ##n## nodes and ##b## edges. We know there are ##m = b - n + 1## fundamental circuits.

Which is the total number of nonempty circuits or edge-disjoint unions of circuits ? If we do not take in account the circuit orientation I believe the answer is ##2^m - 1##.

Is the above correct ? Thanks.

cianfa72 · Jun 7, 2023

To be more specific consider the following graph with 2 nodes and 4 edges. We have 3 fundamental circuits, but which is the total number of circuits or edge-disjoint unions of circuits ?

I Circuits or edge-disjoint unions of circuits in a connected graph

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