Draw the required graph or explain why no such graph exists: 8-vertex, 2 component, simple graph with exactly 10 edges and three cycles.
- I think there is a graph but I'm not sure. Can anyone help to know the answer of this question?
2026-04-01 02:07:15.1775009235
How to know if a graph exists or not?
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Hint. Assume that such a graph exists and see what you can figure out about it. Maybe you will arrive at a contradiction, proving that no such graph exists; failing that, knowing some conditions the graph has to satisfy will narrow down the search for an example.
Hint. There are exactly $8$ vertices, $10$ edges, and $3$ cycles. If you delete $3$ edges, one from each cycle, you will be left with a graph with $8$ vertices, $7$ edges, and no cycles. What do you know about a graph with $n$ vertices, $n-1$ edges, and no cycles? How many components can it have?