Related papers: Effective resistance on random electrical networks

This paper has been withdrawn due to crucial errors.

A modified version of this paper is under process and with a new title and abstract. Hence, this version of the article is completely withdrawn.

The paper has been withdrawn by the author due to a gap in Proof of Theorem 1.1.

This paper has been withdrawn due to an incorrect proof.

This paper has been withdrawn by the author. There is an error on page 3 in the last inequality before Lemma 1.1.

This paper has been withdrawn by the author due to some errors.

This paper has been withdrawn by the author because Lemma 3 is incorrect. This mistake is crucial in this paper.

The paper has been withdrawn due to a crucial error in section 3.

There is a technical issue in the analysis that is not easily fixable. We, therefore, withdraw the submission. Sorry for the inconvenience.

This paper has been withdrawn by the author due to an error in the proof of Theorem 1.

This paper has been withdrawn by the author due to an error in the last paragraph of step 2 of the main proof, on page 6.

This paper has been withdrawn.

This paper has been withdrawn by the author due to a crucial sign error in Proposition 3.1.

This paper has been withdrawn due to that the same conclusion has been proposed before.

This paper has been withdrawn by the author due to a crucial sign error in equation 1

This paper has been withdrawn by the authors as they feel it inappropriate to publish this paper for the time being.

This paper has been withdrawn due to a critical error discovered in Theorem 4.21. Anyone with a historical or pragamatic interest in prior "negative results", however - e.g., failed proof attempts relating to the (in)consistency of ZF or…

This paper has been withdrawn to provide a more rigorous proof of the converse of Theorem 1 and Lemma 1 as well.

This paper has been withdrawn by the author due to a crucial sign error in equation 1

This paper has been withdrawn.