graph 1 3 Sections Graphs Doc

Def df-traversal(G;s) == (i:Vertices(G), s1,s2:traversal(G). s = (s1 @ [inr(i)] @ s2) traversal(G) (j:Vertices(G). (inr(j) s2) (inl(j) s2) j-G- > *i)) & (i:Vertices(G), s1,s2:traversal(G). (j:Vertices(G). i-G- > *j non-trivial-loop(G;j)) s = (s1 @ [inl(i)] @ s2) traversal(G) (j:Vertices(G). i-G- > *j (inr(j) s2)))

is mentioned by

Thm* For any graph the_obj:GraphObject(the_graph). paren(V;depthfirst(the_obj)) & no_repeats(V+V;depthfirst(the_obj)) & df-traversal(the_graph;depthfirst(the_obj)) & depthfirst-traversal(the_graph;depthfirst(the_obj)) & (i:V. (inr(i) depthfirst(the_obj)) & (inl(i) depthfirst(the_obj)))[depthfirst-properties]
Thm* For any graph the_obj:GraphObject(the_graph). df-traversal(the_graph;depthfirst(the_obj))[depthfirst-df-traversal]
Thm* For any graph the_obj:GraphObject(the_graph), s:Traversal, i:V. df-traversal(the_graph;s) (j:V. (inr(j) s) (inl(j) s) j-the_graph- > *i) df-traversal(the_graph;dfs(the_obj;s;i))[dfs-df-traversal]

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graph 1 3 Sections Graphs Doc