(a) Let T be a tree with vertices of degree 1 and 3 only. If T has 10 vertices of degree 3, how many vertices does it have of degree 1?
(b) Let G be a connected graph with n vertices and n edges. How many cycles does G have?
(c) How many leaves in a complete 3-ary tree with 10 internal nodes?
could someone explain to me how to do those plz. thanks!
c)At each level of the tree you are tripling the number of nodes you have. But the tree is not complete. You can make a complete tree up till the 9th level and then count the remaining nodes as they are. The upper nodes will form a diverging geometric series with common ratio equal to 3.