Width of a tree is defined as the largest distance(number of edges in the shortest path) between any two vertices. What is the smallest possible width of the tree with 100 vertices? 1 2 99 101 1 point How many complete graphs with at least 1 edge and at most 50 edges are there? 8 9 10 11
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(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.