Depth algorithm - graph - DEFS

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When applying the adjoining list algorithm in depth search - DFS with a set of vertices and their adjoining ones, the algorithm presents a result, if it changes the order of adjacent ones of at least one vertex, the result is another. That is, the vertices visited in the algorithm have their visitation order changed according to the order of the adjacent vertices of a given vertex.

I wonder if the vertices visited should be the same, independent of the input order of the adjacent vertices of a given vertex to generate the adjacency list?

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