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Shahrooz
Shahrooz
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From NS-equivalentequivalent graphs to isomorphic one- Reconstruction Conjecture

Suppose we are working with connected simple graphs.

We say the graph $G$ is NS-equivalent toand $H$ (NS stands for non-symmetric)are equivalent if for any spanning tree $T_G$ in $G$ there is an spanning tree $T_H$ in $H$ such that $T_G$ is isomorphic to $T_H$ and vice versa.

Can we say that if $G$ is NS-equivalent toand $H$ are equivalent, then they are isomorphic?

The motivation of this question goes back to the reconstruction conjecture. I want to say that if we have $G$ is NS-equivalent toand $H$ or vice versa,are equivalent and RC is true for one of these graphs, then it is true for other one.

From NS-equivalent graphs to isomorphic one- Reconstruction Conjecture

Suppose we are working with connected simple graphs.

We say the graph $G$ is NS-equivalent to $H$ (NS stands for non-symmetric) if for any spanning tree $T_G$ in $G$ there is an spanning tree $T_H$ in $H$ such that $T_G$ is isomorphic to $T_H$.

Can we say that if $G$ is NS-equivalent to $H$, then they are isomorphic?

The motivation of this question goes back to the reconstruction conjecture. I want to say that if we have $G$ is NS-equivalent to $H$ or vice versa, and RC is true for one of these graphs, then it is true for other one.

From equivalent graphs to isomorphic one- Reconstruction Conjecture

Suppose we are working with connected simple graphs.

We say the graph $G$ and $H$ are equivalent if for any spanning tree $T_G$ in $G$ there is an spanning tree $T_H$ in $H$ such that $T_G$ is isomorphic to $T_H$ and vice versa.

Can we say that if $G$ and $H$ are equivalent, then they are isomorphic?

The motivation of this question goes back to the reconstruction conjecture. I want to say that if $G$ and $H$ are equivalent and RC is true for one of these graphs, then it is true for other one.

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Shahrooz
Shahrooz
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From semiNS-equivalent graphs to isomorphic one- Reconstruction Conjecture

Suppose we are working with connected simple graphs.

We say two graphsthe graph $G$ andis NS-equivalent to $H$ are semi(NS stands for non-equivalentsymmetric) if for any spanning tree $T_G$ in $G$ there is an spanning tree $T_H$ in $H$ such that $T_G$ is isomorphic to $T_H$, or vice versa.

Can we say that if $G$ andis NS-equivalent to $H$ are semi_equivalent, then they are isomorphic?

The motivation of this question goes back to the reconstruction conjecture. I want to say that if the two graphs we have $G$ and $H$ are semiis NS-equivalent to $H$ or vice versa, and RC is true for one of themthese graphs, then it is true for other one.

From semi-equivalent graphs to isomorphic one- Reconstruction Conjecture

Suppose we are working with connected simple graphs.

We say two graphs $G$ and $H$ are semi-equivalent if for any spanning tree $T_G$ in $G$ there is an spanning tree $T_H$ in $H$ such that $T_G$ is isomorphic to $T_H$, or vice versa.

Can we say that if $G$ and $H$ are semi_equivalent, then they are isomorphic?

The motivation of this question goes back to the reconstruction conjecture. I want to say that if the two graphs $G$ and $H$ are semi-equivalent and RC is true for one of them, then is true for other one.

From NS-equivalent graphs to isomorphic one- Reconstruction Conjecture

Suppose we are working with connected simple graphs.

We say the graph $G$ is NS-equivalent to $H$ (NS stands for non-symmetric) if for any spanning tree $T_G$ in $G$ there is an spanning tree $T_H$ in $H$ such that $T_G$ is isomorphic to $T_H$.

Can we say that if $G$ is NS-equivalent to $H$, then they are isomorphic?

The motivation of this question goes back to the reconstruction conjecture. I want to say that if we have $G$ is NS-equivalent to $H$ or vice versa, and RC is true for one of these graphs, then it is true for other one.

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Shahrooz
Shahrooz
  • 4.8k
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  • 36

From equivalentsemi-equivalent graphs to isomorphic one- Reconstruction Conjecture

Suppose we are working with connected simple graphs.

We say two graphs $G$ and $H$ are equivalentsemi-equivalent if for any spanning tree $T_G$ in $G$ there is an spanning tree $T_H$ in $H$ such that $T_G$ is isomorphic to $T_H$, or vice versa.

Can we say that if $G$ and $H$ are equivalentsemi_equivalent, then they are isomorphic?

The motivation of this question goes back to the reconstruction conjecture. I want to say that if the reconstruction conjecturetwo graphs $G$ and $H$ are semi-equivalent and RC is true for $G$one of them, then it is true for all graphs which are equivalent to $G$other one.

From equivalent graphs to isomorphic one- Reconstruction Conjecture

Suppose we are working with connected simple graphs.

We say two graphs $G$ and $H$ are equivalent if for any spanning tree $T_G$ in $G$ there is an spanning tree $T_H$ in $H$ such that $T_G$ is isomorphic to $T_H$.

Can we say that if $G$ and $H$ are equivalent, then they are isomorphic?

The motivation of this question goes back to the reconstruction conjecture. I want to say that if the reconstruction conjecture is true for $G$, then it is true for all graphs which are equivalent to $G$.

From semi-equivalent graphs to isomorphic one- Reconstruction Conjecture

Suppose we are working with connected simple graphs.

We say two graphs $G$ and $H$ are semi-equivalent if for any spanning tree $T_G$ in $G$ there is an spanning tree $T_H$ in $H$ such that $T_G$ is isomorphic to $T_H$, or vice versa.

Can we say that if $G$ and $H$ are semi_equivalent, then they are isomorphic?

The motivation of this question goes back to the reconstruction conjecture. I want to say that if the two graphs $G$ and $H$ are semi-equivalent and RC is true for one of them, then is true for other one.

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Shahrooz
Shahrooz
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