05 March 2023   7:58:06.263 PM
 
graph_arc_test():
  FORTRAN90 version
  graph_arc() implements graph algorithms.
 
graph_arc_chromatic_test():
  graph_arc_chromatic() finds the chromatic polynomial
  of a graph.
 
  The end point arrays:
 
   1   1   1   1   2   2   2   3   3   4   4   5
   2   3   4   5   3   4   6   5   6   5   6   6
 
  The chromatic polynomial:
 
  Power sum form:
  64 154 137  58  12   1
 
  Tutte or tree form:
   0  11  25  20   7   1
 
  Stirling form:
   0   0   1   3   3   1
 
graph_arc_complement_test():
  graph_arc_complement() computes the complement
  of a graph described by its edge array;
 
  Number of edges in original graph is        0
  Number of nodes is        0
 
  The graph:
 
Number of edges in complement is        0
 
  The complement graph:
 
 
graph_arc_degree_test():
  graph_arc_degree() computes the degree of the nodes;
 
  The graph:
 
       1           1       3
       2           1       7
       3           1      10
       4           2       5
       5           2      10
       6           3       6
       7           3       9
       8           4       7
       9           4       8
      10           6       9
      11           8      10
 
  The node degrees:
 
       1         3
       2         2
       3         3
       4         2
       5         1
       6         2
       7         2
       8         2
       9         2
      10         3
 
graph_arc_edge_con2_test():
  graph_arc_edge_con2() finds graph edge connectivity.
 
  The arc list of the graph:
 
       1           6       8
       2           2       5
       3           3       1
       4           6       3
       5           7       2
       6           1       8
       7           4       3
       8           7       5
       9           3       8
      10           4       1
      11           9       2
      12           6       1
      13           5       9
      14           4       8
      15           2       6
      16           9       7
      17           4       2
 
  The computed edge connectivity is        2
 
graph_arc_edge_sort_test():
  graph_arc_edge_sort() sorts the edge array of a graph.
 
  Number of edges in original graph is        0
  Number of nodes is        0
 
  The graph:
 
 
graph_arc_euler_circ_test():
  graph_arc_euler_circ() returns an Euler circuit
  of a graph.
 
  The graph:
 
       1           1       2
       2           1       3
       3           1       4
       4           1       5
       5           2       3
       6           2       4
       7           2       5
       8           3       4
       9           3       5
      10           4       5
 
  The nodes in the Euler circuit:
 
       1         1
       2         2
       3         3
       4         4
       5         5
       6         3
       7         1
       8         4
       9         2
      10         5
 
graph_arc_euler_circ_next_test():
  graph_arc_euler_circ_next() finds the next
  Euler circuit of a graph.
 
 
  The graph:
 
       1           1       2
       2           1       3
       3           1       4
       4           1       5
       5           2       3
       6           2       4
       7           2       5
       8           3       4
       9           3       5
      10           4       5
 
  Circuits:
 
  1    1  7 10  8  9  4  3  6  5  2
  2    1  7 10  8  9  4  2  5  6  3
  3    1  7 10  8  2  6  5  9  4  3
  4    1  7 10  8  2  3  4  9  5  6
  5    1  7 10  3  9  8  6  5  2  4
  6    1  7 10  3  9  5  6  8  2  4
 
graph_arc_is_eulerian_test()
  graph_arc_is_eulerian() checks if a graph has an
  Euler circuit.
 
  The graph:
 
       1           1       2
       2           1       3
       3           1       4
       4           1       5
       5           2       3
       6           2       4
       7           2       5
       8           3       4
       9           3       5
      10           4       5
 
  The graph is eulerian.
 
  Circuits:
 
  1    1  7 10  8  9  4  3  6  5  2
  2    1  7 10  8  9  4  2  5  6  3
  3    1  7 10  8  2  6  5  9  4  3
  4    1  7 10  8  2  3  4  9  5  6
  5    1  7 10  3  9  8  6  5  2  4
  6    1  7 10  3  9  5  6  8  2  4
 
graph_arc_match_test():
  graph_arc_match() finds a maximal matching in a graph.
 
  The edge list of the graph:
 
       1           6       2
       2           9       7
       3           3       7
       4           4      10
       5          11       5
       6           6       8
       7           4       6
       8           5       7
       9           6      12
      10          10       2
      11           3       1
      12           4       2
      13           1       5
      14           3       5
 
  Nodes and their types:
 
       1         1
       2         1
       3         2
       4         1
       5         2
       6         2
       7         1
       8         2
       9         2
      10         2
      11         1
      12         1
 
  Node and matching node:
 
       1         3
       2         6
       3         1
       4        10
       5        11
       6         2
       7         9
       8         0
       9         7
      10         4
      11         5
      12         0
 
graph_arc_min_path_test():
  graph_arc_min_path() computes the shortest path from one
  node to another.
 
 
  The weighted graph:
 
       1           1       2   1.00000    
       2           1       3   1.00000    
       3           2       3   3.00000    
       4           2       5   2.00000    
       5           3       4   2.00000    
       6           3       5   5.00000    
 
  The distance matrix constructed by GRAPH_ARC_MIN_PATH:
 
 
 
Columns       1             2             3             4             5       
  Row
 
    1     0.0          1.00000       1.00000       3.00000       3.00000    
    2    1.00000        0.0          2.00000       4.00000       2.00000    
    3    1.00000       2.00000        0.0          2.00000       4.00000    
    4    3.00000       4.00000       2.00000        0.0          6.00000    
    5    3.00000       2.00000       4.00000       6.00000        0.0       
 
  The routine actually also computes the path.
  For instance, starting at node        4
  we compute the shortest path to node        5
 
  The path:
 
       1         4
       2         3
       3         1
       4         2
       5         5
 
graph_arc_min_span_tree_test():
  graph_arc_min_span_tree() finds a minimum length
  spanning tree.
 
 
  The weighted graph:
 
       1           1       2   100.000    
       2           1       3   125.000    
       3           1       4   120.000    
       4           1       5   110.000    
       5           2       3   40.0000    
       6           2       4   65.0000    
       7           2       5   60.0000    
       8           3       4   45.0000    
       9           3       5   55.0000    
      10           4       5   50.0000    
 
  The minimal spanning tree:
 
       1           1       2   100.000    
       2           2       3   40.0000    
       3           3       4   45.0000    
       4           4       5   50.0000    
 
  The length of the minimal tree is    235.000    
 
graph_arc_node_count_test():
  graph_arc_node_count() counts the nodes and
  finds the highest label.
 
  The graph:
 
       1           1       3
       2           1       7
       3           1     100
       4           2       5
       5           2     100
       6           3       0
       7           3       9
       8          -4       7
       9          -4      88
      10           0       9
      11          88     100
  Number of nodes is          10
  Maximum node label is      100
 
graph_arc_span_forest_test():
  graph_arc_span_forest()
  computes a spanning forest for a graph
 
  The graph:
 
       1           2       3
       2           4       7
       3           1       9
       4           7      11
       5           5       8
       6           2       5
       7           6      10
       8           2       8
       9           3       8
      10           4      11
 
  The reordered endpoint array:
 
       1           1       9
       2           2       3
       3           2       5
       4           2       8
       5           4       7
       6           4      11
       7           6      10
       8          11       7
       9           8       3
      10           8       5
 
  Number of connected components =        7
 
  Node component membership:
 
       1         1
       2         2
       3         2
       4         3
       5         2
       6         4
       7         3
       8         2
       9         1
      10         4
      11         3
      12         5
      13         6
      14         7
 
graph_arc_span_tree_test():
  graph_arc_span_tree() constructs a spanning tree.
 
 
  The graph:
 
       1           1       2
       2           1       3
       3           1       4
       4           1       5
       5           1       6
       6           1       7
       7           1       8
       8           2       5
       9           2       6
      10           2       8
      11           3       4
      12           3       7
      13           9      10
      14           9      13
      15          10      11
      16          10      12
      17          10      13
      18          11      12
 
  Nodes and Parent Nodes:
 
       1        -1
       2         1
       3         1
       4         1
       5         1
       6         1
       7         1
       8         1
       9        -1
      10         9
      11        10
      12        10
      13         9
 
graph_arc_to_digraph_arc_test():
  graph_arc_to_digraph_arc() makes a directed graph
  from an undirected one.
 
  The graph:
 
       1           1       2
       2           1       1
       3           1       4
       4           2       1
       5           3       2
       6           4       1
       7           2       3
       8           4       2
 
  The digraph:
 
       1           1       1
       2           1       2
       3           1       4
       4           2       1
       5           2       3
       6           2       4
       7           3       2
       8           4       1
       9           4       2
 
graph_arc_to_graph_adj_test():
  graph_arc_to_graph_adj() converts an arclist
  graph to an adjacency graph.
 
 
  The graph:
 
       1           1       2
       2           1       1
       3           1       4
       4           2       1
       5           3       2
       6           4       1
       7           2       3
       8           4       2
 
  The graph:
 
    1  11010
    2  10110
    3  01000
    4  11000
    5  00000
 
graph_theory_test():
  Normal end of execution.
 
05 March 2023   7:58:06.263 PM