I am going to identify tree edges and back edges in an undirected graph.
The graph consists of $5$ nodes, the edges between these nodes are as shown below:
Suppose starting with $v_1$, after a depth-first searching, what are tree edges and back edges?
My back edges are edge $(v_4,v_2)$ and edge $(v_5,v_2)$, but the textbook says edge $(v_3,v_2)$ and edge $(v_5,v_2)$ are back edges.
My traverse order is $v_1\to v_2\to v_3\to v_4\to v_5$; it seems the traversal order in the textbook is $v_1\to v_2\to v_4\to v_3\to v_5$?
I am confused with the textbook result, And I can not figure out where is the different result from?
Please teach me. Thanks!