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Start by picking an arbitrary node (vertex) as the starting point of the traversal. This node will be the root of the spanning tree.

From the starting point, traverse the graph using DFS by visiting each connected node in depth-first order. Follow this process by visiting the adjacent nodes recursively: 1. Mark the current node as visited. 2. For each adjacent node, if it is not visited yet, visit it recursively by applying DFS.

As we visit each node during DFS traversal, each recursive call represents an edge in the spanning tree. Whenever we visit a new node in the DFS, we can add an edge between the visited node and its parent (the node from which we came). In this way, we can construct the spanning tree while performing DFS traversal. After going through all the nodes and constructing the spanning tree, the output will be a tree that includes all the vertices of the graph while preserving their relative order. Note that there may be more than one valid spanning tree for a given graph, as the final tree depends on the order in which nodes are visited during the DFS traversal. Let's implement the above steps to an example graph with the following adjacency list: Graph: ``` A: B, C B: A, D, E C: A, F, G D: B E: B, H F: C G: C H: E ``` Starting from the node `A`: Spanning tree (using DFS): ``` A ├── B │ ├── D │ └── E │ └── H └── C ├── F └── G ``` Note: This is one possible outcome depending on the order of visiting nodes during the DFS traversal.