eularian circuit

Question

Suppose a connected graph has 15 labeled nodes, given that it has an eularian circuit, what is the minimum number of distinct circuits which it must have? [Note : the circuit a->b->c->a is not same as b->c->a->b]

Comments

Take an example of cycle graph,you will get 2n euler circuits, since labels are distinct else n.

Answer 1

Few information the question has given us: 15 label nodes (therefore order matter) ; euler circuit exist (every node has even degree) ; ;  minimum number of distinct circuit we have to find (from this we can say each node have degree 2).

so to choose starting vertex from 15 labelled nodes we have 15C1 = 15 ways, and after this we have 2 direction to traverse the graph so 2 choices.

therefore the answer is 15*2= 30