In an unweighted, undirected connected graph, the shortest path from a node S to every other node is computed most efficiently, in terms of time complexity by

Consider the following graph: Which one of the following cannot be the sequence of edges added, in that order, to a minimum spanning tree using Kruskal’s algorithm?

Suppose we run Dijkstra’s single source shortest-path algorithm on the following edge-weighted directed graph with vertex P as the source.
In what order do the nodes get included into the set of vertices for which the shortest path distances are finalized?

Let G=(V,E) be an undirected graph with a subgraph G₁=(V₁,E₁). Weights are assigned to edges of G as follows. $$$w(e) = \begin{cases} 0 \text{, if } e \in E_1 \\1 \text{, otherwise} \end{cases}$$$ A single-source shortest path algorithm is executed on the weighted graph (V,E,w) with an arbitrary vertex v1 of V₁ as the source. Which of the following can always be inferred from the path costs computed?