Added proper description for LexUP

src/doc/en/reference/references/index.rst

@@ -3122,6 +3122,10 @@ REFERENCES:
 .. [Mil2004] Victor S. Miller, "The Weil pairing, and its
              efficient calculation", J. Cryptol., 17(4):235-261, 2004
 
+.. [Mil2017] Arthur Milchior, *(Quasi-)linear time algorithm to compute
+             LexDFS, LexUP and LexDown orderings*. (2017)
+             :arxiv:`1701.00305`
+
 .. [MirMor2009] \R. Miranda, D.R. Morrison, "Embeddings of Integral Quadratic Forms"
                 http://www.math.ucsb.edu/~drm/manuscripts/eiqf.pdf .
 

src/sage/graphs/traversals.pyx

@@ -217,11 +217,14 @@ def lex_UP(G, reverse=False, tree=False, initial_vertex=None):
     This algorithm maintains for each vertex left in the graph a code
     corresponding to the vertices already removed. The vertex of maximal
     code (according to the lexicographic order) is then removed, and the
-    codes are updated.
+    codes are updated. During the `i`-th iteration of the algorithm `i` is
+    appended to the codes of all neighbors of the selected vertex that left in
+    the graph
 
     Time complexity is `O(n+m)` where `n` is the number of vertices and `m` is
     the number of edges.
 
+    See [Mil2017]_ for more details on the algorithm.
 
     EXAMPLES: