Question

a connected graph has 64 even vertices and no odd vertices. determine whether the graph has an euler path (but not an euler circuit), an euler circuit, or neither an euler path nor an euler circuit, and explain why. the described graph has:
○ an euler circuit.
○ neither an euler path nor an euler circuit.
○ an euler path (but not an euler circuit).

Explanation:

According to Euler's theorem, a connected graph has an Euler circuit if and only if all vertices have even degrees (i.e., 0 odd - degree vertices). A connected graph has an Euler path (but not an Euler circuit) if and only if it has exactly 2 odd - degree vertices. In this case, the graph has 0 odd - degree vertices.

Answer:

an Euler circuit.