The Answer to the Question
is below this banner.
Here's the Solution to this Question
(1) Consider a graph called star. This graph is a special kind of tree with one internal node and k leaves and has the smallest possible width. A star has 99 edges and 100 vertices and its width is 2.
(2) The complete graph on n vertices has . In order to answer that question, we need to solve equation for positive integer n:
Therefore, there are 9 complete graphs with at least 1 edge and at most 50 edges ().
Answer: 9 graphs.