Here is the file containing the map: tenNode.txt
Since this is a small map, I'll go ahead and turn VERBOSE on for these, to show how that works....and give you insights into search dynamics.
Here we go, copied from my console:
Breadth First
Python 3.6.0 (v3.6.0:41df79263a11, Dec 22 2016, 17:23:13)
[GCC 4.2.1 (Apple Inc. build 5666) (dot 3)] on darwin
z=Searcher('BREADTH','tenNode.txt', hSLD,True)
Loaded search type BREADTH with map in file: tenNode.txt
z.setStartGoal('f','d')
z.go()
BREADTH search: from F to ['D']
Exploring node: F
inserting new children: ['A', 'G']
Open list: ['A;1;79; 0.00;79.00', 'G;1;22; 0.00;22.00']
Exploring node: A
inserting new children: ['B', 'I', 'J']
Open list: ['G;1;22; 0.00;22.00', 'B;2;174; 0.00;174.00', 'I;2;132; 0.00;132.00', 'J;2;118; 0.00;118.00']
Exploring node: G
inserting new children: ['B', 'C', 'I']
Open list: ['B;2;174; 0.00;174.00', 'I;2;132; 0.00;132.00', 'J;2;118; 0.00;118.00', 'C;2;58; 0.00;58.00']
Exploring node: B
inserting new children: ['I']
Open list: ['I;2;132; 0.00;132.00', 'J;2;118; 0.00;118.00', 'C;2;58; 0.00;58.00']
Exploring node: I
inserting new children: ['C', 'D', 'H']
Open list: ['J;2;118; 0.00;118.00', 'C;2;58; 0.00;58.00', 'D;3;258; 0.00;258.00', 'H;3;181; 0.00;181.00']
Exploring node: J
inserting new children: ['E', 'H']
Open list: ['C;2;58; 0.00;58.00', 'D;3;258; 0.00;258.00', 'H;3;181; 0.00;181.00', 'E;3;150; 0.00;150.00']
Exploring node: C
inserting new children: ['D']
Open list: ['D;3;258; 0.00;258.00', 'H;3;181; 0.00;181.00', 'E;3;150; 0.00;150.00']
Exploring node: D
Success! Reached goal node D with path: ['F', 'A', 'I', 'D']
------------------------
SEARCH SUMMARY STATS:
Search Type: BREADTH. Map file: tenNode.txt Total Nodes in Graph:10
Start node: F ; Goal node(s): ['D']
Searched total of 8 nodes out of total of 10 in graph
Ended at Node: D with path cost: 258
Path (4): ['F', 'A', 'I', 'D']
Frontier size: Average= 2.12 ; Max size= 3
Depth of search: Average= 1.62 ; Max Depth= 3
Average branching factor= 3.12
Order of Node Expansion: ['F', 'A', 'G', 'B', 'I', 'J', 'C', 'D']
Depth First
DEPTH search: from F to ['D']
Exploring node: F
inserting new children: ['A', 'G']
Open list: ['A;1;79; 0.00;79.00', 'G;1;22; 0.00;22.00']
Exploring node: A
inserting new children: ['B', 'I', 'J']
Open list: ['B;2;174; 0.00;174.00', 'I;2;132; 0.00;132.00', 'J;2;118; 0.00;118.00', 'G;1;22; 0.00;22.00']
Exploring node: B
inserting new children: ['G', 'I']
Open list: ['G;3;193; 0.00;193.00', 'I;3;205; 0.00;205.00', 'J;2;118; 0.00;118.00']
Exploring node: G
inserting new children: ['C', 'I']
Open list: ['C;4;229; 0.00;229.00', 'I;4;235; 0.00;235.00', 'J;2;118; 0.00;118.00']
Exploring node: C
inserting new children: ['D', 'I']
Open list: ['D;5;366; 0.00;366.00', 'I;5;296; 0.00;296.00', 'J;2;118; 0.00;118.00']
Exploring node: D
Success! Reached goal node D with path: ['F', 'A', 'B', 'G', 'C', 'D']
------------------------
SEARCH SUMMARY STATS:
Search Type: DEPTH. Map file: tenNode.txt Total Nodes in Graph:10
Start node: F ; Goal node(s): ['D']
Searched total of 6 nodes out of total of 10 in graph
Ended at Node: D with path cost: 366
Path (6): ['F', 'A', 'B', 'G', 'C', 'D']
Frontier size: Average= 1.67 ; Max size= 3
Depth of search: Average= 2.50 ; Max Depth= 5
Average branching factor= 2.67
Order of Node Expansion: ['F', 'A', 'B', 'G', 'C', 'D']
Best First
BEST search: from F to ['D']
Exploring node: F
inserting new children: ['A', 'G']
Open list: ['G;1;22; 0.00;22.00', 'A;1;79; 0.00;79.00']
Exploring node: G
inserting new children: ['B', 'C', 'I']
Open list: ['B;2;41; 0.00;41.00', 'C;2;58; 0.00;58.00', 'I;2;64; 0.00;64.00', 'A;1;79; 0.00;79.00']
Exploring node: B
inserting new children: ['A', 'I']
Open list: ['C;2;58; 0.00;58.00', 'I;2;64; 0.00;64.00', 'A;1;79; 0.00;79.00']
Exploring node: C
inserting new children: ['D', 'I']
Open list: ['I;2;64; 0.00;64.00', 'A;1;79; 0.00;79.00', 'D;3;195; 0.00;195.00']
Exploring node: I
inserting new children: ['A', 'D', 'H']
Open list: ['A;1;79; 0.00;79.00', 'H;3;113; 0.00;113.00', 'D;3;190; 0.00;190.00']
Exploring node: A
inserting new children: ['J']
Open list: ['H;3;113; 0.00;113.00', 'J;2;118; 0.00;118.00', 'D;3;190; 0.00;190.00']
Exploring node: H
inserting new children: ['E', 'J']
Open list: ['J;2;118; 0.00;118.00', 'E;4;144; 0.00;144.00', 'D;3;190; 0.00;190.00']
Exploring node: J
inserting new children: ['E']
Open list: ['E;4;144; 0.00;144.00', 'D;3;190; 0.00;190.00']
Exploring node: E
inserting new children: ['D']
Open list: ['D;3;190; 0.00;190.00']
Exploring node: D
Success! Reached goal node D with path: ['F', 'G', 'I', 'D']
------------------------
SEARCH SUMMARY STATS:
Search Type: BEST. Map file: tenNode.txt Total Nodes in Graph:10
Start node: F ; Goal node(s): ['D']
Searched total of 10 nodes out of total of 10 in graph
Ended at Node: D with path cost: 190
Path (4): ['F', 'G', 'I', 'D']
Frontier size: Average= 1.50 ; Max size= 3
Depth of search: Average= 2.00 ; Max Depth= 4
Average branching factor= 3.10
Order of Node Expansion: ['F', 'G', 'B', 'C', 'I', 'A', 'H', 'J', 'E', 'D']
A* with SLD heuristic
A* search: from F to ['D']
Exploring node: F
inserting new children: ['A', 'G']
Open list: ['G;1;22;172.00;194.00', 'A;1;79;163.71;242.71']
Exploring node: G
inserting new children: ['B', 'C', 'I']
Open list: ['I;2;64;130.06;194.06', 'B;2;41;170.06;211.06', 'C;2;58;156.19;214.19', 'A;1;79;163.71;242.71']
Exploring node: I
inserting new children: ['A', 'B', 'C', 'D', 'H']
Open list: ['D;3;190; 0.00;190.00', 'B;2;41;170.06;211.06', 'C;2;58;156.19;214.19', 'H;3;113;103.45;216.45', 'A;1;79;163.71;242.71']
Exploring node: D
Success! Reached goal node D with path: ['F', 'G', 'I', 'D']
------------------------
SEARCH SUMMARY STATS:
Search Type: A*. Map file: tenNode.txt Total Nodes in Graph:10
Using h-function:<function hSLD at 0x1149a09d8>
Start node: F ; Goal node(s): ['D']
Searched total of 4 nodes out of total of 10 in graph
Ended at Node: D with path cost: 190
Path (4): ['F', 'G', 'I', 'D']
Frontier size: Average= 2.00 ; Max size= 4
Depth of search: Average= 1.50 ; Max Depth= 3
Average branching factor= 3.00
Order of Node Expansion: ['F', 'G', 'I', 'D']