Question about isomorphism between two graphs
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If two graphs are isomorphic then does there always exist one vertex $uin A,vin B$ such that removal of this vertices from respective graphs still gives isomorphism? I tried to find contradiction by example with no success.Then I think it is possible every time by picking maximum degree vertex from both and remove it. Am I right?
graph-theory
edited Nov 17 at 1:36
Parcly Taxel
41k137198
asked Nov 17 at 1:11
Believer
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add a comment |
up vote
1
down vote
favorite
If two graphs are isomorphic then does there always exist one vertex $uin A,vin B$ such that removal of this vertices from respective graphs still gives isomorphism? I tried to find contradiction by example with no success.Then I think it is possible every time by picking maximum degree vertex from both and remove it. Am I right?
graph-theory
edited Nov 17 at 1:36
Parcly Taxel
41k137198
asked Nov 17 at 1:11
Believer
451214
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
If two graphs are isomorphic then does there always exist one vertex $uin A,vin B$ such that removal of this vertices from respective graphs still gives isomorphism? I tried to find contradiction by example with no success.Then I think it is possible every time by picking maximum degree vertex from both and remove it. Am I right?
graph-theory
edited Nov 17 at 1:36
Parcly Taxel
41k137198
asked Nov 17 at 1:11
Believer
451214
If two graphs are isomorphic then does there always exist one vertex $uin A,vin B$ such that removal of this vertices from respective graphs still gives isomorphism? I tried to find contradiction by example with no success.Then I think it is possible every time by picking maximum degree vertex from both and remove it. Am I right?
graph-theory
graph-theory
edited Nov 17 at 1:36
Parcly Taxel
41k137198
asked Nov 17 at 1:11
Believer
451214
edited Nov 17 at 1:36
Parcly Taxel
41k137198
asked Nov 17 at 1:11
Believer
451214
edited Nov 17 at 1:36
Parcly Taxel
41k137198
edited Nov 17 at 1:36
Parcly Taxel
41k137198
edited Nov 17 at 1:36
Parcly Taxel
41k137198
41k137198
asked Nov 17 at 1:11
Believer
451214
asked Nov 17 at 1:11
Believer
451214
asked Nov 17 at 1:11
Believer
451214
451214
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
up vote
0
down vote
accepted
Let $f:V_Ato V_B$ be a bijection between the vertices of $A$ and those of $B$. Because this is an isomorphism, any subset of vertices $A'in V_A$ induces a subgraph isomorphic to that induced by $B'=f(A')in V_B$. In the case where $A'$ contains all but one vertex, the desired conclusion is obtained.
answered Nov 17 at 1:21
Parcly Taxel
41k137198
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
Let $f:V_Ato V_B$ be a bijection between the vertices of $A$ and those of $B$. Because this is an isomorphism, any subset of vertices $A'in V_A$ induces a subgraph isomorphic to that induced by $B'=f(A')in V_B$. In the case where $A'$ contains all but one vertex, the desired conclusion is obtained.
answered Nov 17 at 1:21
Parcly Taxel
41k137198
add a comment |
up vote
0
down vote
accepted
Let $f:V_Ato V_B$ be a bijection between the vertices of $A$ and those of $B$. Because this is an isomorphism, any subset of vertices $A'in V_A$ induces a subgraph isomorphic to that induced by $B'=f(A')in V_B$. In the case where $A'$ contains all but one vertex, the desired conclusion is obtained.
answered Nov 17 at 1:21
Parcly Taxel
41k137198
add a comment |
up vote
0
down vote
accepted
up vote
0
down vote
accepted
Let $f:V_Ato V_B$ be a bijection between the vertices of $A$ and those of $B$. Because this is an isomorphism, any subset of vertices $A'in V_A$ induces a subgraph isomorphic to that induced by $B'=f(A')in V_B$. In the case where $A'$ contains all but one vertex, the desired conclusion is obtained.
answered Nov 17 at 1:21
Parcly Taxel
41k137198
Let $f:V_Ato V_B$ be a bijection between the vertices of $A$ and those of $B$. Because this is an isomorphism, any subset of vertices $A'in V_A$ induces a subgraph isomorphic to that induced by $B'=f(A')in V_B$. In the case where $A'$ contains all but one vertex, the desired conclusion is obtained.
answered Nov 17 at 1:21
Parcly Taxel
41k137198
answered Nov 17 at 1:21
Parcly Taxel
41k137198
answered Nov 17 at 1:21
Parcly Taxel
41k137198
answered Nov 17 at 1:21
Parcly Taxel
41k137198
41k137198
add a comment |
add a comment |
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