I answered all questions. I just need a few minutes to write them down.
Just to let you know, one possible answer to the first question is u2-u6-u5-u1-u3-u4-u2
hello I have a degree in mathematics in 2010 graduated from the Central University of Venezuela (UCV), the main university in my country, I am currently doing my masters thesis in mathematics in the area of algebra and algebraic theory of numbers. Since 2010 I am working in the School of Mathematics of the Faculty of Sciences of the UCV. I can do this work please contact me and tell me to when you need the issues and how I will send you the solution of the problems
I have done courses in Graph theory and algebraic graph theory and solved many problems from Harary and Bondy and Murty. Will be able to solve all the problems. e.q. one answer of the 1st problem should be the cycle v_1-v_6-v_2-v_4-v_5-v_3-v_1. Let's see if I can work for you. Thanks.