5. Using Rosen (2012, Theorems 1 p. 696, 2 p. 697), explain whether the undirected graph underlying the graph in Problem 1 has an Euler circuit, and Euler path without an Euler circuit, or neither. points Answer: Explanation: THEOREM 1 A connected multigraph with at least two vertices has an Euler circuit if and only if each of its vertices has even degree. THEOREM 2 A connccted multigraph has an Eulcr path but not an Euler circuit if and only if it has cxactly two vertices of odd degree