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Contributor affiliations
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- By Frank Andrasik, Melissa R. Andrews, Ana Inés Ansaldo, Evangelos G. Antzoulatos, Lianhua Bai, Ellen Barrett, Linamara Battistella, Nicolas Bayle, Michael S. Beattie, Peter J. Beek, Serafin Beer, Heinrich Binder, Claire Bindschaedler, Sarah Blanton, Tasia Bobish, Michael L. Boninger, Joseph F. Bonner, Chadwick B. Boulay, Vanessa S. Boyce, Anna-Katharine Brem, Jacqueline C. Bresnahan, Floor E. Buma, Mary Bartlett Bunge, John H. Byrne, Jeffrey R. Capadona, Stefano F. Cappa, Diana D. Cardenas, Leeanne M. Carey, S. Thomas Carmichael, Glauco A. P. Caurin, Pablo Celnik, Kimberly M. Christian, Stephanie Clarke, Leonardo G. Cohen, Adriana B. Conforto, Rory A. Cooper, Rosemarie Cooper, Steven C. Cramer, Armin Curt, Mark D’Esposito, Matthew B. Dalva, Gavriel David, Brandon Delia, Wenbin Deng, Volker Dietz, Bruce H. Dobkin, Marco Domeniconi, Edith Durand, Tracey Vause Earland, Georg Ebersbach, Jonathan J. Evans, James W. Fawcett, Uri Feintuch, Toby A. Ferguson, Marie T. Filbin, Diasinou Fioravante, Itzhak Fischer, Agnes Floel, Herta Flor, Karim Fouad, Richard S. J. Frackowiak, Peter H. Gorman, Thomas W. Gould, Jean-Michel Gracies, Amparo Gutierrez, Kurt Haas, C.D. Hall, Hans-Peter Hartung, Zhigang He, Jordan Hecker, Susan J. Herdman, Seth Herman, Leigh R. Hochberg, Ahmet Höke, Fay B. Horak, Jared C. Horvath, Richard L. Huganir, Friedhelm C. Hummel, Beata Jarosiewicz, Frances E. Jensen, Michael Jöbges, Larry M. Jordan, Jon H. Kaas, Andres M. Kanner, Noomi Katz, Matthew S. Kayser, Annmarie Kelleher, Gerd Kempermann, Timothy E. Kennedy, Jürg Kesselring, Fary Khan, Rachel Kizony, Jeffery D. Kocsis, Boudewijn J. Kollen, Hubertus Köller, John W. Krakauer, Hermano I. Krebs, Gert Kwakkel, Bradley Lang, Catherine E. Lang, Helmar C. Lehmann, Angelo C. Lepore, Glenn S. Le Prell, Mindy F. Levin, Joel M. Levine, David A. Low, Marilyn MacKay-Lyons, Jeffrey D. Macklis, Margaret Mak, Francine Malouin, William C. Mann, Paul D. Marasco, Christopher J. Mathias, Laura McClure, Jan Mehrholz, Lorne M. Mendell, Robert H. Miller, Carol Milligan, Beth Mineo, Simon W. Moore, Jennifer Morgan, Charbel E-H. Moussa, Martin Munz, Randolph J. Nudo, Joseph J. Pancrazio, Theresa Pape, Alvaro Pascual-Leone, Kristin M. Pearson-Fuhrhop, P. Hunter Peckham, Tamara L. Pelleshi, Catherine Verrier Piersol, Thomas Platz, Marcus Pohl, Dejan B. Popović, Andrew M. Poulos, Maulik Purohit, Hui-Xin Qi, Debbie Rand, Mahendra S. Rao, Josef P. Rauschecker, Aimee Reiss, Carol L. Richards, Keith M. Robinson, Melvyn Roerdink, John C. Rosenbek, Serge Rossignol, Edward S. Ruthazer, Arash Sahraie, Krishnankutty Sathian, Marc H. Schieber, Brian J. Schmidt, Michael E. Selzer, Mijail D. Serruya, Himanshu Sharma, Michael Shifman, Jerry Silver, Thomas Sinkjær, George M. Smith, Young-Jin Son, Tim Spencer, John D. Steeves, Oswald Steward, Sheela Stuart, Austin J. Sumner, Chin Lik Tan, Robert W. Teasell, Gareth Thomas, Aiko K. Thompson, Richard F. Thompson, Wesley J. Thompson, Erika Timar, Ceri T. Trevethan, Christopher Trimby, Gary R. Turner, Mark H. Tuszynski, Erna A. van Niekerk, Ricardo Viana, Difei Wang, Anthony B. Ward, Nick S. Ward, Stephen G. Waxman, Patrice L. Weiss, Jörg Wissel, Steven L. Wolf, Jonathan R. Wolpaw, Sharon Wood-Dauphinee, Ross D. Zafonte, Binhai Zheng, Richard D. Zorowitz
- Edited by Michael Selzer, Stephanie Clarke, Leonardo Cohen, Gert Kwakkel, Robert Miller, Case Western Reserve University, Ohio
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- Book:
- Textbook of Neural Repair and Rehabilitation
- Published online:
- 05 May 2014
- Print publication:
- 24 April 2014, pp ix-xvi
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Contributor affiliations
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- By Frank Andrasik, Melissa R. Andrews, Ana Inés Ansaldo, Evangelos G. Antzoulatos, Lianhua Bai, Ellen Barrett, Linamara Battistella, Nicolas Bayle, Michael S. Beattie, Peter J. Beek, Serafin Beer, Heinrich Binder, Claire Bindschaedler, Sarah Blanton, Tasia Bobish, Michael L. Boninger, Joseph F. Bonner, Chadwick B. Boulay, Vanessa S. Boyce, Anna-Katharine Brem, Jacqueline C. Bresnahan, Floor E. Buma, Mary Bartlett Bunge, John H. Byrne, Jeffrey R. Capadona, Stefano F. Cappa, Diana D. Cardenas, Leeanne M. Carey, S. Thomas Carmichael, Glauco A. P. Caurin, Pablo Celnik, Kimberly M. Christian, Stephanie Clarke, Leonardo G. Cohen, Adriana B. Conforto, Rory A. Cooper, Rosemarie Cooper, Steven C. Cramer, Armin Curt, Mark D’Esposito, Matthew B. Dalva, Gavriel David, Brandon Delia, Wenbin Deng, Volker Dietz, Bruce H. Dobkin, Marco Domeniconi, Edith Durand, Tracey Vause Earland, Georg Ebersbach, Jonathan J. Evans, James W. Fawcett, Uri Feintuch, Toby A. Ferguson, Marie T. Filbin, Diasinou Fioravante, Itzhak Fischer, Agnes Floel, Herta Flor, Karim Fouad, Richard S. J. Frackowiak, Peter H. Gorman, Thomas W. Gould, Jean-Michel Gracies, Amparo Gutierrez, Kurt Haas, C.D. Hall, Hans-Peter Hartung, Zhigang He, Jordan Hecker, Susan J. Herdman, Seth Herman, Leigh R. Hochberg, Ahmet Höke, Fay B. Horak, Jared C. Horvath, Richard L. Huganir, Friedhelm C. Hummel, Beata Jarosiewicz, Frances E. Jensen, Michael Jöbges, Larry M. Jordan, Jon H. Kaas, Andres M. Kanner, Noomi Katz, Matthew S. Kayser, Annmarie Kelleher, Gerd Kempermann, Timothy E. Kennedy, Jürg Kesselring, Fary Khan, Rachel Kizony, Jeffery D. Kocsis, Boudewijn J. Kollen, Hubertus Köller, John W. Krakauer, Hermano I. Krebs, Gert Kwakkel, Bradley Lang, Catherine E. Lang, Helmar C. Lehmann, Angelo C. Lepore, Glenn S. Le Prell, Mindy F. Levin, Joel M. Levine, David A. Low, Marilyn MacKay-Lyons, Jeffrey D. Macklis, Margaret Mak, Francine Malouin, William C. Mann, Paul D. Marasco, Christopher J. Mathias, Laura McClure, Jan Mehrholz, Lorne M. Mendell, Robert H. Miller, Carol Milligan, Beth Mineo, Simon W. Moore, Jennifer Morgan, Charbel E-H. Moussa, Martin Munz, Randolph J. Nudo, Joseph J. Pancrazio, Theresa Pape, Alvaro Pascual-Leone, Kristin M. Pearson-Fuhrhop, P. Hunter Peckham, Tamara L. Pelleshi, Catherine Verrier Piersol, Thomas Platz, Marcus Pohl, Dejan B. Popović, Andrew M. Poulos, Maulik Purohit, Hui-Xin Qi, Debbie Rand, Mahendra S. Rao, Josef P. Rauschecker, Aimee Reiss, Carol L. Richards, Keith M. Robinson, Melvyn Roerdink, John C. Rosenbek, Serge Rossignol, Edward S. Ruthazer, Arash Sahraie, Krishnankutty Sathian, Marc H. Schieber, Brian J. Schmidt, Michael E. Selzer, Mijail D. Serruya, Himanshu Sharma, Michael Shifman, Jerry Silver, Thomas Sinkjær, George M. Smith, Young-Jin Son, Tim Spencer, John D. Steeves, Oswald Steward, Sheela Stuart, Austin J. Sumner, Chin Lik Tan, Robert W. Teasell, Gareth Thomas, Aiko K. Thompson, Richard F. Thompson, Wesley J. Thompson, Erika Timar, Ceri T. Trevethan, Christopher Trimby, Gary R. Turner, Mark H. Tuszynski, Erna A. van Niekerk, Ricardo Viana, Difei Wang, Anthony B. Ward, Nick S. Ward, Stephen G. Waxman, Patrice L. Weiss, Jörg Wissel, Steven L. Wolf, Jonathan R. Wolpaw, Sharon Wood-Dauphinee, Ross D. Zafonte, Binhai Zheng, Richard D. Zorowitz
- Edited by Michael E. Selzer, Stephanie Clarke, Leonardo G. Cohen, Gert Kwakkel, Robert H. Miller, Case Western Reserve University, Ohio
-
- Book:
- Textbook of Neural Repair and Rehabilitation
- Published online:
- 05 June 2014
- Print publication:
- 24 April 2014, pp ix-xvi
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- Chapter
- Export citation
Minimal line graphs
- David P. Sumner
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- Journal:
- Glasgow Mathematical Journal / Volume 17 / Issue 1 / January 1976
- Published online by Cambridge University Press:
- 18 May 2009, pp. 12-16
- Print publication:
- January 1976
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In this paper all graphs will be ordinary graphs, i.e. finite, undirected, and without loops or multiple edges. For points x and y of a graph G, we shall indicate that x is adjacent to y by writing x ⊥ y, and if x is not adjacent to y we shall write xy. We shall denote the degree of a point x by δ(x) and the minimal degree of G by δ(G).
By the line graph of a graph G we shall mean the graph L(G) whose points are the edges of G, with two points of L(G) adjacent whenever they are adjacent in G. A graph G is said to be a line graph if there exists a graph H such that G = L(H).
Dacey Graphs
- David P. Sumner
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- Journal:
- Journal of the Australian Mathematical Society (1959) / Volume 18 / Issue 4 / December 1974
- Published online by Cambridge University Press:
- 09 April 2009, pp. 492-502
- Print publication:
- December 1974
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In this paper our graphs will be finite, undirected, and without loops or multiple edges. We will denote the set of vertices of a graph G by V(G). If G is a graph and u, v∈V(G), then we will write u ∼ v to denote that u and v are adjacent and u ≁ v otherwise. If A ⊆ V(G), then we let N(A) = {u∈ V(G)|u ∼ a for each a ∈A}. However we write N(v) instead of N({v}). When there is no chance of confusion, we will not distinguish between a subset A ⊆ V(G) of vertices of G and the subgraph that it induces. We will denote the cardinality of a set A by |A|. The degree of a vertex v is δ(v) = |N(v)|. Any undefined terminology in this paper will generally conform with Behzad and Chartrand [1].