%0 Journal Article %1 lier73 %A van Lier, M. %A Otten, R. %D 1973 %J IEEE Transactions on Circuit Theory %K graph graph.theory kron planar %N 2 %P 169--171 %R 10.1109/TCT.1973.1083633 %T Planarization by Transformation %V 20 %X A new approach to star-polygon transformations is introduced. For star-connected <img src="/images/tex/1065.gif" alt="R"> -networks and for a certain class of polygon-connected <img src="/images/tex/1065.gif" alt="R"> -networks the "terminal value" is defined. This concept allows for an elegant derivation of the necessary and sufficient conditions for the existence of a polygon-into-star transformation. The related formulas appear to be simple and easy to remember. More important, the terminal value turns out to be a useful tool in the search for planar equivalents and in the recognition of transformable polygon structures. Simplicity is the only reason for the restriction to resistance networks. The study of the general RLC case does not bring out any new aspects.

@article{lier73, abstract = {A new approach to star-polygon transformations is introduced. For star-connected <img src="/images/tex/1065.gif" alt="R"> -networks and for a certain class of polygon-connected <img src="/images/tex/1065.gif" alt="R"> -networks the "terminal value" is defined. This concept allows for an elegant derivation of the necessary and sufficient conditions for the existence of a polygon-into-star transformation. The related formulas appear to be simple and easy to remember. More important, the terminal value turns out to be a useful tool in the search for planar equivalents and in the recognition of transformable polygon structures. Simplicity is the only reason for the restriction to resistance networks. The study of the general RLC case does not bring out any new aspects.}, added-at = {2016-05-22T08:52:36.000+0200}, author = {van Lier, M. and Otten, R.}, biburl = {https://www.bibsonomy.org/bibtex/279068ff7328c299b274f51fb0b1401c4/ytyoun}, doi = {10.1109/TCT.1973.1083633}, interhash = {17e15e437008a0bc954c57500103635a}, intrahash = {79068ff7328c299b274f51fb0b1401c4}, issn = {0018-9324}, journal = {IEEE Transactions on Circuit Theory}, keywords = {graph graph.theory kron planar}, month = mar, number = 2, pages = {169--171}, timestamp = {2016-05-22T08:52:36.000+0200}, title = {Planarization by Transformation}, volume = 20, year = 1973 }