Below are four different questions with the correct result given. However, the calculations for how we derive the results are missing. The task of whom who accepts this question is to show thoroughly the missing calculations for each of the four sub-questions.

A graph G with vertices Vi, 22, ..., 37 has adjacency matrix TO 101000] 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1. Answer the following true/false problems. G has an Euler circuit True False G has a Hamilton circuit True False G has a Hamilton path True False 2. What is the length of the shortest simple circuit in G? 01 02 03 +4 05 06 07 3. What is the number of edges of a spanning tree of G? 00 01 02 03 04 05 06 07 08 09