Question

Which route must use all of the vertices of a vertex-edge graph? (Check all that apply.)

Hamilton path
Euler path
Euler circuit
Hamilton circuit

Answer 1

your answer is wrong but good example but the right answer is

Hamilton Path and Hamilton Circuit not Euler Path or Euler Circuit

Answer 2

An Euler path, in a graph or multi graph, is a walk through the graph which uses every edge exactly once. An Euler circuit is an Euler path which starts and stops at the same vertex. Our goal is to find a quick way to check whether a graph (or multi graph) has an Euler path or circuit.

hope it helps