Non-isomorphic connected bipartite simple graphs
0
$begingroup$
How many non-isomorphic connected bipartite simple graphs are there with four vertices?
I got below 3.
Numerically my answer is valid. But is it logically valid?
graph-theory
asked Dec 25 '18 at 5:43
user3767495user3767495
3888
$endgroup$
add a comment |
0
$begingroup$
How many non-isomorphic connected bipartite simple graphs are there with four vertices?
I got below 3.
Numerically my answer is valid. But is it logically valid?
graph-theory
asked Dec 25 '18 at 5:43
user3767495user3767495
3888
$endgroup$
$begingroup$
What was your logic? You've not written how you reached here
$endgroup$
– Ankit Kumar
Dec 25 '18 at 6:11
$begingroup$
Looks correct if you don't care about which named node has which 'function'. For example, in your left example, there are 3 more isomorphic versions were B, C, and D take the 'central place' that A has in your example. Those are isomorphic, but depending on why you need to consider this problem, those might still count as different. See for example en.wikipedia.org/wiki/Cayley%27s_formula, which deals with 'labeled' trees, which is obviously different from the question of unlabled trees.
$endgroup$
– Ingix
Dec 25 '18 at 9:30
add a comment |
0
0
0
$begingroup$
How many non-isomorphic connected bipartite simple graphs are there with four vertices?
I got below 3.
Numerically my answer is valid. But is it logically valid?
graph-theory
asked Dec 25 '18 at 5:43
user3767495user3767495
3888
$endgroup$
How many non-isomorphic connected bipartite simple graphs are there with four vertices?
I got below 3.
Numerically my answer is valid. But is it logically valid?
graph-theory
graph-theory
asked Dec 25 '18 at 5:43
user3767495user3767495
3888
asked Dec 25 '18 at 5:43
user3767495user3767495
3888
asked Dec 25 '18 at 5:43
user3767495user3767495
3888
asked Dec 25 '18 at 5:43
user3767495user3767495
3888
asked Dec 25 '18 at 5:43
user3767495user3767495
3888
3888
$begingroup$
What was your logic? You've not written how you reached here
$endgroup$
– Ankit Kumar
Dec 25 '18 at 6:11
$begingroup$
Looks correct if you don't care about which named node has which 'function'. For example, in your left example, there are 3 more isomorphic versions were B, C, and D take the 'central place' that A has in your example. Those are isomorphic, but depending on why you need to consider this problem, those might still count as different. See for example en.wikipedia.org/wiki/Cayley%27s_formula, which deals with 'labeled' trees, which is obviously different from the question of unlabled trees.
$endgroup$
– Ingix
Dec 25 '18 at 9:30
add a comment |
$begingroup$
What was your logic? You've not written how you reached here
$endgroup$
– Ankit Kumar
Dec 25 '18 at 6:11
$begingroup$
Looks correct if you don't care about which named node has which 'function'. For example, in your left example, there are 3 more isomorphic versions were B, C, and D take the 'central place' that A has in your example. Those are isomorphic, but depending on why you need to consider this problem, those might still count as different. See for example en.wikipedia.org/wiki/Cayley%27s_formula, which deals with 'labeled' trees, which is obviously different from the question of unlabled trees.
$endgroup$
– Ingix
Dec 25 '18 at 9:30
$begingroup$
What was your logic? You've not written how you reached here
$endgroup$
– Ankit Kumar
Dec 25 '18 at 6:11
$begingroup$
What was your logic? You've not written how you reached here
$endgroup$
– Ankit Kumar
Dec 25 '18 at 6:11
$begingroup$
Looks correct if you don't care about which named node has which 'function'. For example, in your left example, there are 3 more isomorphic versions were B, C, and D take the 'central place' that A has in your example. Those are isomorphic, but depending on why you need to consider this problem, those might still count as different. See for example en.wikipedia.org/wiki/Cayley%27s_formula, which deals with 'labeled' trees, which is obviously different from the question of unlabled trees.
$endgroup$
– Ingix
Dec 25 '18 at 9:30
$begingroup$
Looks correct if you don't care about which named node has which 'function'. For example, in your left example, there are 3 more isomorphic versions were B, C, and D take the 'central place' that A has in your example. Those are isomorphic, but depending on why you need to consider this problem, those might still count as different. See for example en.wikipedia.org/wiki/Cayley%27s_formula, which deals with 'labeled' trees, which is obviously different from the question of unlabled trees.
$endgroup$
– Ingix
Dec 25 '18 at 9:30
add a comment |
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$begingroup$
What was your logic? You've not written how you reached here
$endgroup$
– Ankit Kumar
Dec 25 '18 at 6:11
$begingroup$
Looks correct if you don't care about which named node has which 'function'. For example, in your left example, there are 3 more isomorphic versions were B, C, and D take the 'central place' that A has in your example. Those are isomorphic, but depending on why you need to consider this problem, those might still count as different. See for example en.wikipedia.org/wiki/Cayley%27s_formula, which deals with 'labeled' trees, which is obviously different from the question of unlabled trees.
$endgroup$
– Ingix
Dec 25 '18 at 9:30