I'm a novice in Graph Theory. I would like to know the set of minimum number of properties of a connected graph with no loops, uniquely. For example: the count of vertices and the count of edges do constitute the bare minimum. Those 2 numbers may help you to infer if the graph has a circuit or not (|E|-|V| = 1 means acyclic; |E|-|V| = 0 means cyclic;). Are there additional bare minimum number properties?

Thank you in advance.

Velu

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