1NAUTY-WATERCLUSTER2(1) Nauty Manual NAUTY-WATERCLUSTER2(1)
2
6 nauty-watercluster2 - generate small digraphs with given underlying
7 graph (faster alternative to directg)
8
10 watercluster2 [ix] [oy] [S] [T] [B] [Z] [C] [m]
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13 Reads graphs in g6 code or multicode (optional) from stdin and
14 directs them
15 ix: the indegree of every vertex may be at most x.
17 The default maximum indegree is unlimited.
19 oy: the outdegree of every vertex may be at most y.
21 The default maximum outdegree is unlimited.
23 S : allow that for every pair of vertices x,y at most one of the
25 edges x-->y
26 and y-->x may be present. By default both of them may be present
28 in the same graph.
29 T : Output directed graphs in T-code. This is a simple ASCII
31 output format.
32 Every line contains one graph. First the number of vertices,
34 then the number of directed edges and then the list of directed
35 edges with the start first and the end then. E.g.: 3 2 0 1 2 1
36 means 3 vertices, 2 directed edges: 0-->1 and 2-->1
37 B : Output the directed graphs in a binary code. Every item of
39 the code is an
40 unsigned char. The first unsigned char is the number nv of ver‐
42 tices. The vertices are numbered 1..nv. Then the list of ver‐
43 tices x for which there is a directed edge 1->x follow. This
44 list is ended by a 0. Then the list of outgoing neighbours of 2
45 follows -- again ended with a 0, etc. The code is complete with
46 the 0 ending the list of outgoing neighbours of nv.
47 Z : Output the directed graphs in digraph6 code. See formats.txt
49 for a
50 complete definition.
52 C : Do really construct all the directed graphs in memory, but
54 don't output
55 them. This is not a big difference in case of restricted in- and
57 outdegrees, because all that is done extra is that edges are di‐
58 rected instead of just keeping track of in- and out-degrees.
59 This option is intended only for testing purposes to test also
60 routines that are normally not used when counting. Things that
61 would speed up the counting also in some cases of restricted in-
62 and out-degrees -- like multiplying the possibilities of assign‐
63 ing directions to edges that can be assigned directions indepen‐
64 dent of each other (depending on the degrees of the endvertices
65 and overlaps) -- are not included. In case of not restrictive
66 bounds on the in- and out-degree it not really constructing the
67 graphs can be considerably faster. In cases of restricted in-
68 and out-degrees the only difference is that the graph isn't mod‐
69 ified. The fact that in case of no output the graph is not mod‐
70 ified is mainly to save time for the one case of waterclusters,
71 where large numbers were determined. If large numbers (without
72 output) for other cases shall be determined, one should think
73 about adding the multiplication routines.
74 m : read multicode instead of g6 code
76 This program uses different labelling routines -- all based on the
78 ideas of
79 G. Brinkmann, Generating water clusters and other directed
81 graphs,mJournal of Mathematical Chemistry 46, 1112--1121 (2009)
82nauty 2.8.6 September 2023 NAUTY-WATERCLUSTER2(1)