1. The n-cube, denoted by Qn, is the graph that has 2n vertices representing the bit strings of length n. Two vertices are adjacent if they differ in exactly one-bit position (bit flip). Show by example that for Q2 and Q3 (see figure below), the minimum number of vertices to remove to cause the graph to become disconnected is n. (2pts) 2. Using the graph Q3 write one distinct and nontrivial example for each of the following: trail, path, closed walks, circuits, simple circuits. (1 pts) 3. For which values of n can an n-cube have an Eulerian circuit? (1pt)