List of practice Questions

Consider a simple undirected weighted graph \(G\), all of whose edge weights are distinct. Which of the following statements about the minimum spanning trees of \(G\) is/are TRUE?

Let \(G\) be a connected undirected weighted graph. Consider the following two statements:
\(S_1:\) There exists a minimum weight edge in \(G\) which is present in every minimum spanning tree of \(G\).
\(S_2:\) If every edge in \(G\) has distinct weight, then \(G\) has a unique minimum spanning tree.
Which one of the following options is correct?

Consider the following undirected graph with edge weights as shown. The number of minimum-weight spanning trees of the graph is \(\underline{\hspace{2cm}}\).