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?

The following simple undirected graph is referred to as the Peterson graph.

Which of the following statements is/are TRUE?

Which of the properties hold for the adjacency matrix A of a simple undirected unweighted graph having n vertices?

Which of the following is/are the eigenvector(s) for the matrix given below?

$$\left( {\matrix{ { - 9} & { - 6} & { - 2} & { - 4} \cr { - 8} & { - 6} & { - 3} & { - 1} \cr {20} & {15} & 8 & 5 \cr {32} & {21} & 7 & {12} \cr } } \right)$$