%0 Journal Article
%T The Rupture Degree of Graphs with <i>k</i>-Tree
%A Yinkui Li
%A Qingning Wang
%A Xiaoling Wang
%J Open Journal of Discrete Mathematics
%P 105-107
%@ 2161-7643
%D 2016
%I Scientific Research Publishing
%R 10.4236/ojdm.2016.62011
%X A <i>k-</i>tree of a connected graph <i>G</i> is a spanning tree with maximum degree
at most <i>k</i>. The rupture degree for a
connected graph <i>G</i> is defined by <img src=\"Edit_b58fa23a-98ff-4199-911e-76bc4b4ef859.bmp\" alt=\"\" /><span lang=\"TR\">, where <img src=\"Edit_35922f6e-2272-4632-87a9-ed52c8561fe6.bmp\" alt=\"\" /></span><span lang=\"TR\"> and <img src=\"Edit_e6b09751-5959-4a77-b685-17d31303ae86.bmp\" alt=\"\" /></span><span lang=\"TR\">,
respectively, denote the order of the largest component and number of
components in <img src=\"Edit_077131f4-f132-41b4-a5cd-66b88bc66cf9.bmp\" alt=\"\" /></span><span lang=\"TR\">. In this
paper, we show that for a connected graph <i>G</i>,
if <img src=\"Edit_e19ec7e8-d1ad-4c74-866c-373648242933.bmp\" alt=\"\" />&nbsp;</span><span lang=\"TR\">for any cut-set <img src=\"Edit_1a990dd6-5334-49a4-89cb-736f7a80aa19.bmp\" alt=\"\" /></span><span lang=\"TR\">, then <i>G</i> has a <i>k-</i>tree.</span>
%K The Rupture Degree
%K &lt
%K i&gt
%K k&lt
%K /i&gt
%K -Tree
%K Induced Graph
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=65755