Does Graph definition carry also labels?
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The slides of my prof. say that two isomorphic graphs, with different labels are the same graph.
This must imply that the definition of a graph doesn't carry the nodes and vertices labels. Is this true ?
graph-theory
asked Aug 27 at 12:10
Koinos
756
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The slides of my prof. say that two isomorphic graphs, with different labels are the same graph.
This must imply that the definition of a graph doesn't carry the nodes and vertices labels. Is this true ?
graph-theory
asked Aug 27 at 12:10
Koinos
756
This depends on how you define a graph.
– Babelfish
Aug 27 at 12:11
1
The definition of a graph does "carry the node and vertex labels." Two graphs being isomorphic just means that you can switch the labels of one graph for the labels of the other, such that the graph "looks the same," i.e. has the same set of vertex-edge indices. Do a few examples if you're still confused. It should become clear.
– Dzoooks
Aug 27 at 12:14
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up vote
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down vote
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up vote
0
down vote
favorite
The slides of my prof. say that two isomorphic graphs, with different labels are the same graph.
This must imply that the definition of a graph doesn't carry the nodes and vertices labels. Is this true ?
graph-theory
asked Aug 27 at 12:10
Koinos
756
The slides of my prof. say that two isomorphic graphs, with different labels are the same graph.
This must imply that the definition of a graph doesn't carry the nodes and vertices labels. Is this true ?
graph-theory
asked Aug 27 at 12:10
Koinos
756
asked Aug 27 at 12:10
Koinos
756
asked Aug 27 at 12:10
Koinos
756
asked Aug 27 at 12:10
Koinos
756
756
This depends on how you define a graph.
– Babelfish
Aug 27 at 12:11
1
The definition of a graph does "carry the node and vertex labels." Two graphs being isomorphic just means that you can switch the labels of one graph for the labels of the other, such that the graph "looks the same," i.e. has the same set of vertex-edge indices. Do a few examples if you're still confused. It should become clear.
– Dzoooks
Aug 27 at 12:14
add a comment |Â
This depends on how you define a graph.
– Babelfish
Aug 27 at 12:11
1
The definition of a graph does "carry the node and vertex labels." Two graphs being isomorphic just means that you can switch the labels of one graph for the labels of the other, such that the graph "looks the same," i.e. has the same set of vertex-edge indices. Do a few examples if you're still confused. It should become clear.
– Dzoooks
Aug 27 at 12:14
This depends on how you define a graph.
– Babelfish
Aug 27 at 12:11
This depends on how you define a graph.
– Babelfish
Aug 27 at 12:11
1
1
The definition of a graph does "carry the node and vertex labels." Two graphs being isomorphic just means that you can switch the labels of one graph for the labels of the other, such that the graph "looks the same," i.e. has the same set of vertex-edge indices. Do a few examples if you're still confused. It should become clear.
– Dzoooks
Aug 27 at 12:14
The definition of a graph does "carry the node and vertex labels." Two graphs being isomorphic just means that you can switch the labels of one graph for the labels of the other, such that the graph "looks the same," i.e. has the same set of vertex-edge indices. Do a few examples if you're still confused. It should become clear.
– Dzoooks
Aug 27 at 12:14
add a comment |Â
1 Answer
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That is very true and convenient.
Since two isomorphic graphs are basically the same graph we do not need to consider labeling into the definition of graph.
However, when we assign an adjacency matrix to a graph, labeling comes to play an important role because isomorphic graphs may
have different adjacency matrices associated to them.
answered Aug 27 at 12:19
Mohammad Riazi-Kermani
30.6k41852
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
That is very true and convenient.
Since two isomorphic graphs are basically the same graph we do not need to consider labeling into the definition of graph.
However, when we assign an adjacency matrix to a graph, labeling comes to play an important role because isomorphic graphs may
have different adjacency matrices associated to them.
answered Aug 27 at 12:19
Mohammad Riazi-Kermani
30.6k41852
add a comment |Â
up vote
0
down vote
That is very true and convenient.
Since two isomorphic graphs are basically the same graph we do not need to consider labeling into the definition of graph.
However, when we assign an adjacency matrix to a graph, labeling comes to play an important role because isomorphic graphs may
have different adjacency matrices associated to them.
answered Aug 27 at 12:19
Mohammad Riazi-Kermani
30.6k41852
add a comment |Â
up vote
0
down vote
up vote
0
down vote
That is very true and convenient.
Since two isomorphic graphs are basically the same graph we do not need to consider labeling into the definition of graph.
However, when we assign an adjacency matrix to a graph, labeling comes to play an important role because isomorphic graphs may
have different adjacency matrices associated to them.
answered Aug 27 at 12:19
Mohammad Riazi-Kermani
30.6k41852
That is very true and convenient.
Since two isomorphic graphs are basically the same graph we do not need to consider labeling into the definition of graph.
However, when we assign an adjacency matrix to a graph, labeling comes to play an important role because isomorphic graphs may
have different adjacency matrices associated to them.
answered Aug 27 at 12:19
Mohammad Riazi-Kermani
30.6k41852
answered Aug 27 at 12:19
Mohammad Riazi-Kermani
30.6k41852
answered Aug 27 at 12:19
Mohammad Riazi-Kermani
30.6k41852
answered Aug 27 at 12:19
Mohammad Riazi-Kermani
30.6k41852
30.6k41852
add a comment |Â
add a comment |Â
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This depends on how you define a graph.
– Babelfish
Aug 27 at 12:11
1
The definition of a graph does "carry the node and vertex labels." Two graphs being isomorphic just means that you can switch the labels of one graph for the labels of the other, such that the graph "looks the same," i.e. has the same set of vertex-edge indices. Do a few examples if you're still confused. It should become clear.
– Dzoooks
Aug 27 at 12:14